<?xml version="1.0" encoding="UTF-8"?>
<strings>
  <sentenca xml:id="Logo">
    <traducao xml:lang="pt-br">ANAWEB - Algoritmos Numéricos e Algébricos na Web</traducao>
    <traducao xml:lang="en-us">ANAWEB - Algebraic and Numerical Algorithms on the Web</traducao>
  </sentenca>
  <sentenca xml:id="Inicio">
    <traducao xml:lang="pt-br">Início</traducao>
    <traducao xml:lang="en-us">Start</traducao>
  </sentenca>
  <sentenca xml:id="Cadastrar">
    <traducao xml:lang="pt-br">Cadastrar</traducao>
    <traducao xml:lang="en-us">Sign up</traducao>
  </sentenca>
  <sentenca xml:id="Email">
    <traducao xml:lang="pt-br">E-mail</traducao>
    <traducao xml:lang="en-us">E-mail</traducao>
  </sentenca>
  <sentenca xml:id="Senha">
    <traducao xml:lang="pt-br">Senha</traducao>
    <traducao xml:lang="en-us">Password</traducao>
  </sentenca>
  <sentenca xml:id="Logar">
    <traducao xml:lang="pt-br">Logar</traducao>
    <traducao xml:lang="en-us">Login</traducao>
  </sentenca>
  <sentenca xml:id="Usuario">
    <traducao xml:lang="pt-br">Usuário</traducao>
    <traducao xml:lang="en-us">User</traducao>
  </sentenca>
  <sentenca xml:id="Minha_Conta">
    <traducao xml:lang="pt-br">Minha Conta</traducao>
    <traducao xml:lang="en-us">My account</traducao>
  </sentenca>
  <sentenca xml:id="Email_ou_Senha_Invalida">
    <traducao xml:lang="pt-br">O e-mail/senha digitada não confere.</traducao>
    <traducao xml:lang="en-us">Invalid e-mail/password combination.</traducao>
  </sentenca>
  <sentenca xml:id="Alterar_Cadastro">
    <traducao xml:lang="pt-br">Alterar cadastro</traducao>
    <traducao xml:lang="en-us">Update account</traducao>
  </sentenca>
  <sentenca xml:id="Modo_Aluno">
    <traducao xml:lang="pt-br">Modo aluno</traducao>
    <traducao xml:lang="en-us">Learner mode</traducao>
  </sentenca>
  <sentenca xml:id="Modo_Professor">
    <traducao xml:lang="pt-br">Modo professor</traducao>
    <traducao xml:lang="en-us">Teacher mode</traducao>
  </sentenca>
  <sentenca xml:id="Modo_Aprendiz">
    <traducao xml:lang="pt-br">modo aprendiz</traducao>
    <traducao xml:lang="en-us">learner mode</traducao>
  </sentenca>
  <sentenca xml:id="Modo_Autoria">
    <traducao xml:lang="pt-br">modo autoria</traducao>
    <traducao xml:lang="en-us">authoring mode</traducao>
  </sentenca>
  <sentenca xml:id="Ambiente_Numerico">
    <traducao xml:lang="pt-br">ambiente numérico</traducao>
    <traducao xml:lang="en-us">numerical environment</traducao>
  </sentenca>
  <sentenca xml:id="Ambiente_Maple">
    <traducao xml:lang="pt-br">ambiente maple</traducao>
    <traducao xml:lang="en-us">maple environment</traducao>
  </sentenca>
  <sentenca xml:id="Ambiente_Scilab">
    <traducao xml:lang="pt-br">ambiente scilab</traducao>
    <traducao xml:lang="en-us">scilab environment</traducao>
  </sentenca>
  <sentenca xml:id="Sair">
    <traducao xml:lang="pt-br">Sair</traducao>
    <traducao xml:lang="en-us">Logout</traducao>
  </sentenca>
  <sentenca xml:id="Footer">
    <traducao xml:lang="pt-br">Laboratório de Pesquisa PROTEM - Departamento de Computação - UEL</traducao>
    <traducao xml:lang="en-us">Protem Research Laboratory - Computer Department - UEL</traducao>
  </sentenca>
  <sentenca xml:id="Digite_Campos">
    <traducao xml:lang="pt-br">Você deve digitar todos os campos para efetuar o login</traducao>
    <traducao xml:lang="en-us">You must type in all fields to login</traducao>
  </sentenca>
  <sentenca xml:id="Metodos_Numericos">
    <traducao xml:lang="pt-br">Métodos Numéricos</traducao>
    <traducao xml:lang="en-us">Numerical Methods</traducao>
  </sentenca>
  <sentenca xml:id="Gerenciar_Bibliotecas">
    <traducao xml:lang="pt-br">Gerenciar bibliotecas</traducao>
    <traducao xml:lang="en-us">Manage libraries</traducao>
  </sentenca>
  <sentenca xml:id="Enviar_Material_Teorico">
    <traducao xml:lang="pt-br">Enviar Material Teórico</traducao>
    <traducao xml:lang="en-us">Send conceptual material</traducao>
  </sentenca>
  <sentenca xml:id="Colaborar_Biblioteca">
    <traducao xml:lang="pt-br">Colaborar em uma biblioteca</traducao>
    <traducao xml:lang="en-us">Colaborate on a library</traducao>
  </sentenca>
  <sentenca xml:id="Criar_Biblioteca">
    <traducao xml:lang="pt-br">Criar biblioteca</traducao>
    <traducao xml:lang="en-us">Create library</traducao>
  </sentenca>
  <sentenca xml:id="Biblioteca">
    <traducao xml:lang="pt-br">Biblioteca</traducao>
    <traducao xml:lang="en-us">Library</traducao>
  </sentenca>
  <sentenca xml:id="Alterar_Arvore">
    <traducao xml:lang="pt-br">Alterar árvore de tópicos</traducao>
    <traducao xml:lang="en-us">Change topics tree</traducao>
  </sentenca>
  <sentenca xml:id="Nome_Item">
    <traducao xml:lang="pt-br">Nome do item</traducao>
    <traducao xml:lang="en-us">Item name</traducao>
  </sentenca>
  <sentenca xml:id="Comandos">
    <traducao xml:lang="pt-br">Comandos</traducao>
    <traducao xml:lang="en-us">Commands</traducao>
  </sentenca>
  <sentenca xml:id="Arquivo">
    <traducao xml:lang="pt-br">Arquivo</traducao>
    <traducao xml:lang="en-us">File</traducao>
  </sentenca>
  <sentenca xml:id="Descricao">
    <traducao xml:lang="pt-br">Descrição</traducao>
    <traducao xml:lang="en-us">Description</traducao>
  </sentenca>
  <sentenca xml:id="Nova_Pasta">
    <traducao xml:lang="pt-br">Nova pasta</traducao>
    <traducao xml:lang="en-us">New folder</traducao>
  </sentenca>
  <sentenca xml:id="Novo_Item">
    <traducao xml:lang="pt-br">Novo item</traducao>
    <traducao xml:lang="en-us">New item</traducao>
  </sentenca>
  <sentenca xml:id="Remover_Pasta_Item">
    <traducao xml:lang="pt-br">Remover pasta/item</traducao>
    <traducao xml:lang="en-us">Remove folder/item</traducao>
  </sentenca>
  <sentenca xml:id="Nome">
    <traducao xml:lang="pt-br">Nome</traducao>
    <traducao xml:lang="en-us">Name</traducao>
  </sentenca>
  <sentenca xml:id="Arvore_Alterada_Sucesso">
    <traducao xml:lang="pt-br">Árvore alterada com sucesso</traducao>
    <traducao xml:lang="en-us">Tree changed successfuly</traducao>
  </sentenca>
  <sentenca xml:id="Voltar">
    <traducao xml:lang="pt-br">Voltar</traducao>
    <traducao xml:lang="en-us">Go back</traducao>
  </sentenca>
  <sentenca xml:id="Envio_Arquivos">
    <traducao xml:lang="pt-br">Envio de arquivos</traducao>
    <traducao xml:lang="en-us">Upload files</traducao>
  </sentenca>
  <sentenca xml:id="Autor">
    <traducao xml:lang="pt-br">Autor</traducao>
    <traducao xml:lang="en-us">Author</traducao>
  </sentenca>
  <sentenca xml:id="Topico">
    <traducao xml:lang="pt-br">Tópico</traducao>
    <traducao xml:lang="en-us">Topic</traducao>
  </sentenca>
  <sentenca xml:id="Ptoflut">
    <traducao xml:lang="pt-br">Aritmética de Ponto Flutuante</traducao>
    <traducao xml:lang="en-us">Floating Point Arithmetic</traducao>
  </sentenca>
  <sentenca xml:id="Matriz">
    <traducao xml:lang="pt-br">Aritmética Matricial</traducao>
    <traducao xml:lang="en-us">Matricial Arithmetic </traducao>
  </sentenca>
  <sentenca xml:id="Sistemas">
    <traducao xml:lang="pt-br">Sistemas de Equações Algébricas Lineares</traducao>
    <traducao xml:lang="en-us">Systems of Linear Algebraic Equation</traducao>
  </sentenca>
  <sentenca xml:id="Interpolacao">
    <traducao xml:lang="pt-br">Métodos de Interpolação</traducao>
    <traducao xml:lang="en-us">Interpolation Methods</traducao>
  </sentenca>
  <sentenca xml:id="Ajuste_Dados">
    <traducao xml:lang="pt-br">Ajuste de Dados</traducao>
    <traducao xml:lang="en-us">Data Fitting</traducao>
  </sentenca>
  <sentenca xml:id="Reseqnl">
    <traducao xml:lang="pt-br">Resolução de Equaçõo Não Lineares</traducao>
    <traducao xml:lang="en-us">Nonlinear Equations Solving</traducao>
  </sentenca>
  <sentenca xml:id="Siseqnl">
    <traducao xml:lang="pt-br">Sistemas de Equações Algébricas Não-Lineares</traducao>
    <traducao xml:lang="en-us">Systems of Nonlinear Algebraic Equations</traducao>
  </sentenca>
  <sentenca xml:id="Derivada">
    <traducao xml:lang="pt-br">Derivação numerica</traducao>
    <traducao xml:lang="en-us">Numerical Derivative</traducao>
  </sentenca>
  <sentenca xml:id="Integral">
    <traducao xml:lang="pt-br">Integração numerica</traducao>
    <traducao xml:lang="en-us">Numerical Integration</traducao>
  </sentenca>
  <sentenca xml:id="Integrais_Derivadas">
    <traducao xml:lang="pt-br">Integrais e Derivadas</traducao>
    <traducao xml:lang="en-us">Integration and Derivatives</traducao>
  </sentenca>
  <sentenca xml:id="Enviado_Em">
    <traducao xml:lang="pt-br">Enviado em</traducao>
    <traducao xml:lang="en-us">Sent on</traducao>
  </sentenca>
  <sentenca xml:id="Visualisar_Outro_Professor">
    <traducao xml:lang="pt-br">Caso deseje visualisar materiais de outro professor, selecione um deles abaixo:</traducao>
    <traducao xml:lang="en-us">In case you wish to seee another teacher's material, select one of them below:</traducao>
  </sentenca>
  <sentenca xml:id="Material_Nao_Disponivel">
    <traducao xml:lang="pt-br">Seu professor não tem nenhum material disponível para este tópico</traducao>
    <traducao xml:lang="en-us">Your teacher does not have any material available on this topic</traducao>
  </sentenca>
  <sentenca xml:id="Professor_Sem_Material">
    <traducao xml:lang="pt-br">Seu professor não tem nenhum material teórico disponível.</traducao>
    <traducao xml:lang="en-us">Your teacher does not have any material available.</traducao>
  </sentenca>
  <sentenca xml:id="Enviado_Sucesso">
    <traducao xml:lang="pt-br">Arquivo enviado com sucesso!</traducao>
    <traducao xml:lang="en-us">File sent successfuly!</traducao>
  </sentenca>
  <sentenca xml:id="Visualisar_Download">
    <traducao xml:lang="pt-br">Para visualisá-lo clique no link abaixo</traducao>
    <traducao xml:lang="en-us">To view the file, click on the link below</traducao>
  </sentenca>
  <sentenca xml:id="Arquivos_Consulta">
    <traducao xml:lang="pt-br">Arquivos para consulta</traducao>
    <traducao xml:lang="en-us">Files for consult</traducao>
  </sentenca>
  <sentenca xml:id="Topicos_Consulta">
    <traducao xml:lang="pt-br">Selecione o topico para consulta</traducao>
    <traducao xml:lang="en-us">Select the topic for consult</traducao>
  </sentenca>
  <sentenca xml:id="Consultar">
    <traducao xml:lang="pt-br">Consultar</traducao>
    <traducao xml:lang="en-us">Consult</traducao>
  </sentenca>
  <sentenca xml:id="Enviar">
    <traducao xml:lang="pt-br">Enviar</traducao>
    <traducao xml:lang="en-us">Send</traducao>
  </sentenca>
  <sentenca xml:id="Confirma_Excluir_Item">
    <traducao xml:lang="pt-br">Tem certeza que deseja excluir esse item?</traducao>
    <traducao xml:lang="en-us">Are you sure you want to remove this item?</traducao>
  </sentenca>
  <sentenca xml:id="Confirma_Excluir_Pasta">
    <traducao xml:lang="pt-br">Tem certeza que deseja excluir essa pasta e todos os seus conteudos?</traducao>
    <traducao xml:lang="en-us">Are you sure you want to remove this folder and all its contents?</traducao>
  </sentenca>
  <sentenca xml:id="Biblioteca_Utilizada">
    <traducao xml:lang="pt-br">Biblioteca utilizada</traducao>
    <traducao xml:lang="en-us">LIbrary used</traducao>
  </sentenca>
  <sentenca xml:id="Substituicao_Vetor">
    <traducao xml:lang="pt-br">Substituição do vetor solução no sistema original</traducao>
    <traducao xml:lang="en-us">Substituction of the solution vector on the original system</traducao>
  </sentenca>
  <sentenca xml:id="Outros_Exemplos">
    <traducao xml:lang="pt-br">Outros exemplos</traducao>
    <traducao xml:lang="en-us">Other examples</traducao>
  </sentenca>
  <sentenca xml:id="Soma">
    <traducao xml:lang="pt-br">Soma</traducao>
    <traducao xml:lang="en-us">Sum</traducao>
  </sentenca>
  <sentenca xml:id="Divisao">
    <traducao xml:lang="pt-br">Divisão</traducao>
    <traducao xml:lang="en-us">Division</traducao>
  </sentenca>
  <sentenca xml:id="Multiplicacao">
    <traducao xml:lang="pt-br">Multiplicação</traducao>
    <traducao xml:lang="en-us">Multiplication</traducao>
  </sentenca>
  <sentenca xml:id="Subtracao">
    <traducao xml:lang="pt-br">Subtração</traducao>
    <traducao xml:lang="en-us">Subtraction</traducao>
  </sentenca>
  <sentenca xml:id="Computacao_Algebrica">
    <traducao xml:lang="pt-br">Computação Algébrica</traducao>
    <traducao xml:lang="en-us">Algebraic Computation</traducao>
  </sentenca>
  <sentenca xml:id="Dica">
    <traducao xml:lang="pt-br">Dica</traducao>
    <traducao xml:lang="en-us">Hint</traducao>
  </sentenca>
  <sentenca xml:id="Explicacao">
    <traducao xml:lang="pt-br">Explicação</traducao>
    <traducao xml:lang="en-us">Explanation</traducao>
  </sentenca>
  <sentenca xml:id="Exemplo">
    <traducao xml:lang="pt-br">Exemplo</traducao>
    <traducao xml:lang="en-us">Example</traducao>
  </sentenca>
  <sentenca xml:id="Exercicio">
    <traducao xml:lang="pt-br">Exercício</traducao>
    <traducao xml:lang="en-us">Exercise</traducao>
  </sentenca>
  <sentenca xml:id="Ajuda">
    <traducao xml:lang="pt-br">Ajuda</traducao>
    <traducao xml:lang="en-us">Help</traducao>
  </sentenca>
  <sentenca xml:id="Item">
    <traducao xml:lang="pt-br">Item</traducao>
    <traducao xml:lang="en-us">Item</traducao>
  </sentenca>
  <sentenca xml:id="Comando_Relacionado">
    <traducao xml:lang="pt-br">Comando relacionado</traducao>
    <traducao xml:lang="en-us">Related command</traducao>
  </sentenca>
  <sentenca xml:id="Tente_Voce_Mesmo">
    <traducao xml:lang="pt-br">Tente você mesmo</traducao>
    <traducao xml:lang="en-us">Try yourself</traducao>
  </sentenca>
  <sentenca xml:id="Template">
    <traducao xml:lang="pt-br">Template</traducao>
    <traducao xml:lang="en-us">Template</traducao>
  </sentenca>
  <sentenca xml:id="Comentario">
    <traducao xml:lang="pt-br">Comentário</traducao>
    <traducao xml:lang="en-us">Remark</traducao>
  </sentenca>
  <sentenca xml:id="Solucao">
    <traducao xml:lang="pt-br">Solução</traducao>
    <traducao xml:lang="en-us">Solution</traducao>
  </sentenca>
  <sentenca xml:id="Arquivo_Ajuda">
    <traducao xml:lang="pt-br">Arquivo de ajuda</traducao>
    <traducao xml:lang="en-us">Help file</traducao>
  </sentenca>
  <sentenca xml:id="Msg_Ajuda">
    <traducao xml:lang="pt-br">Caso queira ajuda adicional, clique no link abaixo.</traducao>
    <traducao xml:lang="en-us">In case you want aditional help, click on the link below</traducao>
  </sentenca>
  <sentenca xml:id="Comandos_Relacionados">
    <traducao xml:lang="pt-br">Comandos relacionados</traducao>
    <traducao xml:lang="en-us">Related commands</traducao>
  </sentenca>
  <sentenca xml:id="Aviso">
    <traducao xml:lang="pt-br">Aviso</traducao>
    <traducao xml:lang="en-us">Warning</traducao>
  </sentenca>
  <sentenca xml:id="Arquivo_Sera_Sobrescrito">
    <traducao xml:lang="pt-br">caso envie um novo arquivo, o antigo será sobrescrito.</traducao>
    <traducao xml:lang="en-us">if you send a new file, the old file will be overwritten</traducao>
  </sentenca>
  <sentenca xml:id="Grafico">
    <traducao xml:lang="pt-br">Gráfico</traducao>
    <traducao xml:lang="en-us">Graphic</traducao>
  </sentenca>
  <sentenca xml:id="Comando">
    <traducao xml:lang="pt-br">Comando</traducao>
    <traducao xml:lang="en-us">Command</traducao>
  </sentenca>
  <sentenca xml:id="Material_Teorico">
    <traducao xml:lang="pt-br">Material Teórico</traducao>
    <traducao xml:lang="en-us">Conceptual material</traducao>
  </sentenca>
  <sentenca xml:id="Nao_Logado">
    <traducao xml:lang="pt-br">Você não está logado</traducao>
    <traducao xml:lang="en-us">You are not logged on</traducao>
  </sentenca>
  <sentenca xml:id="Nao_Logado_Msg">
    <traducao xml:lang="pt-br">Você não está logado.&lt;br&gt;Por favor, logue-se pelo menu à esquerda.</traducao>
    <traducao xml:lang="en-us">You are not logged on.&lt;br&gt;Please, login to continue</traducao>
  </sentenca>
  <sentenca xml:id="Menu_Aritmetica_Matricial">
    <traducao xml:lang="pt-br">ARITMÉTICA MATRICIAL</traducao>
    <traducao xml:lang="en-us">MATRICIAL ARITHMETIC</traducao>
  </sentenca>
  <sentenca xml:id="Menu_Determinante">
    <traducao xml:lang="pt-br">Determinante (por Gauss)</traducao>
    <traducao xml:lang="en-us">Determinant (by Gauss)</traducao>
  </sentenca>
  <sentenca xml:id="Menu_Inversa">
    <traducao xml:lang="pt-br">Inversa (por Gauss)</traducao>
    <traducao xml:lang="en-us">Inverse (by Gauss)</traducao>
  </sentenca>
  <sentenca xml:id="Menu_Decomposicao">
    <traducao xml:lang="pt-br">Decomposição de matrizes</traducao>
    <traducao xml:lang="en-us">Matrix decomposition</traducao>
  </sentenca>
  <sentenca xml:id="Menu_Matrizes_Definidas_Positivas">
    <traducao xml:lang="pt-br">Matrizes definidas positivas</traducao>
    <traducao xml:lang="en-us">Definite positive matrices</traducao>
  </sentenca>
  <sentenca xml:id="Menu_Multiplicacao">
    <traducao xml:lang="pt-br">Multiplicação</traducao>
    <traducao xml:lang="en-us">Multiplication</traducao>
  </sentenca>
  <sentenca xml:id="Menu_Soma">
    <traducao xml:lang="pt-br">Soma</traducao>
    <traducao xml:lang="en-us">Sum</traducao>
  </sentenca>
  <sentenca xml:id="Menu_Transposta">
    <traducao xml:lang="pt-br">Transposta</traducao>
    <traducao xml:lang="en-us">Transpose</traducao>
  </sentenca>
  <sentenca xml:id="Menu_SEAL">
    <traducao xml:lang="pt-br">SISTEMAS DE EQUAÇÕES ALGÉBRICAS LINEARES</traducao>
    <traducao xml:lang="en-us">SYSTEM OF LINEAR ALGEBRAIC EQUATION</traducao>
  </sentenca>
  <sentenca xml:id="Menu_Metodos_Diretos">
    <traducao xml:lang="pt-br">Métodos Diretos</traducao>
    <traducao xml:lang="en-us">Direct Methods</traducao>
  </sentenca>
  <sentenca xml:id="Menu_Eliminacao_Gauss">
    <traducao xml:lang="pt-br">Eliminação de Gauss</traducao>
    <traducao xml:lang="en-us">Gauss Elimination</traducao>
  </sentenca>
  <sentenca xml:id="Menu_Sem_Pivoteamento">
    <traducao xml:lang="pt-br">Sem pivoteamento</traducao>
    <traducao xml:lang="en-us">Without pivoting</traducao>
  </sentenca>
  <sentenca xml:id="Menu_Pivoteamento_Parcial">
    <traducao xml:lang="pt-br">Pivoteamento parcial</traducao>
    <traducao xml:lang="en-us">Parcial pivoting</traducao>
  </sentenca>
  <sentenca xml:id="Menu_Pivoteamento_Total">
    <traducao xml:lang="pt-br">Pivoteamento total</traducao>
    <traducao xml:lang="en-us">Maximal pivoting</traducao>
  </sentenca>
  <sentenca xml:id="Menu_Decomposicao_LU">
    <traducao xml:lang="pt-br">Decomposição L.U.</traducao>
    <traducao xml:lang="en-us">L.U. Decomposition</traducao>
  </sentenca>
  <sentenca xml:id="Menu_Cholesky">
    <traducao xml:lang="pt-br">Cholesky</traducao>
    <traducao xml:lang="en-us">Cholesky</traducao>
  </sentenca>
  <sentenca xml:id="Menu_Metodos_Iterativos">
    <traducao xml:lang="pt-br">Métodos Iterativos</traducao>
    <traducao xml:lang="en-us">Iterative Methods</traducao>
  </sentenca>
  <sentenca xml:id="Menu_Gauss_Seidel">
    <traducao xml:lang="pt-br">Gauss-Seidel</traducao>
    <traducao xml:lang="en-us">Gauss-Seidel</traducao>
  </sentenca>
  <sentenca xml:id="Menu_Jacobi">
    <traducao xml:lang="pt-br">Jacobi</traducao>
    <traducao xml:lang="en-us">Jacobi</traducao>
  </sentenca>
  <sentenca xml:id="Menu_Interpolacao">
    <traducao xml:lang="pt-br">MÉTODOS DE INTERPOLAÇÃO</traducao>
    <traducao xml:lang="en-us">INTERPOLATION METHODS</traducao>
  </sentenca>
  <sentenca xml:id="Menu_Lagrange">
    <traducao xml:lang="pt-br">Lagrange</traducao>
    <traducao xml:lang="en-us">Lagrange</traducao>
  </sentenca>
  <sentenca xml:id="Menu_Newton">
    <traducao xml:lang="pt-br">Newton</traducao>
    <traducao xml:lang="en-us">Newton</traducao>
  </sentenca>
  <sentenca xml:id="Menu_Splines">
    <traducao xml:lang="pt-br">Splines cúbicos</traducao>
    <traducao xml:lang="en-us">Cubic splines</traducao>
  </sentenca>
  <sentenca xml:id="Menu_Ajuste_Dados">
    <traducao xml:lang="pt-br">AJUSTE DE DADOS</traducao>
    <traducao xml:lang="en-us">DATA FITTING</traducao>
  </sentenca>
  <sentenca xml:id="Menu_Minimos_Quadrados">
    <traducao xml:lang="pt-br">Mínimos quadrados</traducao>
    <traducao xml:lang="en-us">Least Squares Approximation</traducao>
  </sentenca>
  <sentenca xml:id="Menu_EQNL">
    <traducao xml:lang="pt-br">RESOLUÇÃO DE EQUAÇÕES NÃO-LINEARES</traducao>
    <traducao xml:lang="en-us">NONLINEAR EQUATION SOLVING</traducao>
  </sentenca>
  <sentenca xml:id="Menu_EQNL2">
    <traducao xml:lang="pt-br">Resolução de equações não-lineares</traducao>
    <traducao xml:lang="en-us">Nonlinear equation solving</traducao>
  </sentenca>
  <sentenca xml:id="Menu_Bisseccao">
    <traducao xml:lang="pt-br">Método da Bissecção</traducao>
    <traducao xml:lang="en-us">Bisection method</traducao>
  </sentenca>
  <sentenca xml:id="Menu_Secante">
    <traducao xml:lang="pt-br">Método da Secante</traducao>
    <traducao xml:lang="en-us">Secant method</traducao>
  </sentenca>
  <sentenca xml:id="Menu_Newton_EQNL">
    <traducao xml:lang="pt-br">Método de Newton</traducao>
    <traducao xml:lang="en-us">Newton's method</traducao>
  </sentenca>
  <sentenca xml:id="Menu_SEANL">
    <traducao xml:lang="pt-br">SISTEMAS DE EQUAÇÕES ALGÉBRICAS NÃO-LINEARES</traducao>
    <traducao xml:lang="en-us">SYSTEM OF NONLINEAR ALGEBRAIC EQUATION</traducao>
  </sentenca>
  <sentenca xml:id="Menu_Newton_SEANL">
    <traducao xml:lang="pt-br">Método de Newton</traducao>
    <traducao xml:lang="en-us">Newton's method</traducao>
  </sentenca>
  <sentenca xml:id="Menu_Integrais_Derivadas">
    <traducao xml:lang="pt-br">INTEGRAIS E DERIVADAS</traducao>
    <traducao xml:lang="en-us">INTEGRATION AND DERIVATIVES</traducao>
  </sentenca>
  <sentenca xml:id="Menu_Integracao_Numerica">
    <traducao xml:lang="pt-br">Integração numérica</traducao>
    <traducao xml:lang="en-us">Numerical integration</traducao>
  </sentenca>
  <sentenca xml:id="Menu_Richardson">
    <traducao xml:lang="pt-br">Método de Richardson</traducao>
    <traducao xml:lang="en-us">Richardson's method</traducao>
  </sentenca>
  <sentenca xml:id="Menu_Romberg">
    <traducao xml:lang="pt-br">Método de Romberg</traducao>
    <traducao xml:lang="en-us">Romberg's method</traducao>
  </sentenca>
  <sentenca xml:id="Menu_Simpson">
    <traducao xml:lang="pt-br">Método de Simpson</traducao>
    <traducao xml:lang="en-us">Simpson's method</traducao>
  </sentenca>
  <sentenca xml:id="Menu_Trapezio">
    <traducao xml:lang="pt-br">Método do trapézio</traducao>
    <traducao xml:lang="en-us">Trapezoidal method</traducao>
  </sentenca>
  <sentenca xml:id="Menu_EDO">
    <traducao xml:lang="pt-br">EQUAÇÕES DIFERENCIAIS ORIDINÁRIAS</traducao>
    <traducao xml:lang="en-us"/>
  </sentenca>
  <sentenca xml:id="Menu_Derivacao">
    <traducao xml:lang="pt-br">Derivação numérica</traducao>
    <traducao xml:lang="en-us">Numerical derivative</traducao>
  </sentenca>
  <sentenca xml:id="Menu_Diferenca">
    <traducao xml:lang="pt-br">Diferença central</traducao>
    <traducao xml:lang="en-us">Central diference</traducao>
  </sentenca>
  <sentenca xml:id="Menu_Aritmetica_PF">
    <traducao xml:lang="pt-br">ARITMÉTICA DE PONTO FLUTUANTE</traducao>
    <traducao xml:lang="en-us">FLOATING POINT ARITHMETIC</traducao>
  </sentenca>
  <sentenca xml:id="Menu_Sistema_PF">
    <traducao xml:lang="pt-br">Sistema de ponto flutuante</traducao>
    <traducao xml:lang="en-us">Floating point system</traducao>
  </sentenca>
  <sentenca xml:id="Menu_Divisao">
    <traducao xml:lang="pt-br">Divisão</traducao>
    <traducao xml:lang="en-us">Division</traducao>
  </sentenca>
  <sentenca xml:id="Menu_Subtracao">
    <traducao xml:lang="pt-br">Subtração</traducao>
    <traducao xml:lang="en-us">Subtraction</traducao>
  </sentenca>
  <sentenca xml:id="Autorizar_Usuario1">
    <traducao xml:lang="pt-br">O usuário</traducao>
    <traducao xml:lang="en-us">User</traducao>
  </sentenca>
  <sentenca xml:id="Autorizar_Usuario2">
    <traducao xml:lang="pt-br">deseja colaborar nesta biblioteca, deseja permitir que ele a edite?</traducao>
    <traducao xml:lang="en-us">wants to colaborate on this library, do you want to grant him permission to edit this library?</traducao>
  </sentenca>
  <sentenca xml:id="Introducao">
    <traducao xml:lang="pt-br">    &lt;h1&gt;ANA-WEB: Algoritmos Numéricos e Algébricos na Web - Ambiente de apoio a aprendizagem de algoritmos numéricos e algébricos.&lt;/h1&gt;&#13;
    &lt;p&gt;&#13;
        Este ambiente  tem por objetivo prover a execução de programas para Computação&#13;
        Numérica, visando auxiliar no processo de aprendizagem de algoritmos numéricos. O ambiente possui 3&#13;
        níveis de usuário: aprendiz, professor e colaborador. O usuário aprendiz pode navegar entre os diferentes tópicos apresentados&#13;
&#13;
        Para cada tópico apresentado no lado esquerdo da tela,&#13;
        é possível verificar o funcionamento do algoritmo correspondente, através  da execução&#13;
        com explicaçães&#13;
        do método aplicado&#13;
        a problemas  com explicações&#13;
        de exemplos sugeridos por bibliotecas&#13;
        de problemas exemplo ou  formulados pelo aprendiz.&#13;
        O usuário professor pode formular diferentes bibliotecas com problemas exemplos de acordo com as necessidades &#13;
        de diferentes interesses de aprendizes. O usuário colaborador pode realizar tarefas de autoria nas bibliotecas de problemas-&#13;
        exemplo que um usuário  professor tenha autorizado.&#13;
        O sistema permite a integração&#13;
        com sistemas de Computação&#13;
        Matematica como Maple e Scilab, visando oferecer alternativas de&#13;
        recursos computacionais para os alunos desenvolverem seus programas nos tópicos apresentados. Recursos de computação&#13;
        algébrica &#13;
        são providos através destes sistemas, permitindo mesclar manipulação&#13;
        algébrica com c[alculo numérico, visando minimizar os erros&#13;
        decorrentes do uso de um sistema de ponto flutuante.&#13;
        Este trabalho encontra-se em desenvolvimento. Críticas,&#13;
        sugestões e comentários são bem-vindos e podem ser enviados para &lt;a href=mailto:"angelica@uel.br&gt;" angelica@uel.br &lt;/a&gt;&#13;
        &lt;/p&gt;&#13;
        &lt;h2&gt;Equipe: &lt;/h2&gt;&#13;
        &lt;h2&gt;Coordenadora:&lt;/h2&gt; &#13;
        &lt;p&gt;Maria Angélica de Oliveira Camargo Brunetto&lt;/p&gt;&#13;
        &lt;h2&gt;Alunos de Iniciação Científica:&lt;/h2&gt; &#13;
        &lt;h2&gt; Anos Anteriores &lt;/h2&gt;&#13;
        &lt;p&gt;Claiton Oliveira &lt;/p&gt;&#13;
        &lt;p&gt;Cleberson Vidotte Costa &lt;/p&gt;&#13;
        &lt;p&gt;Douglas Terêncio do Vale &lt;/p&gt;&#13;
        &lt;p&gt;Marcelo Manzatto &lt;/p&gt;&#13;
	  &lt;p&gt;Thalita Veronese  &lt;/p&gt;&#13;
        &lt;h2&gt; Período Atual &lt;/h2&gt;&#13;
        &lt;p&gt;Rafael Yul Arabori (2007)&lt;/p&gt;</traducao>
    <traducao xml:lang="en-us">        &lt;h1&gt;ANA-WEB: Algebraic and Numerical Algorithms on the Web - Environment of support on the learning proccess of numerical and algebraic algorithms. &lt;/h1&gt;&#13;
        &lt;p&gt;&#13;
            This environment's objective is to provide the execution of Numerical Computation programs, aiming to help the learning process of numerical algorithms. The environment has 3 user levels: learner, teacher and colaborator. The learner level can browse the different topics presented.&#13;
            It is possible to see the functioning of each algorithm for each presented topic on the left side of the screen through a detailed explanation of the method applied on examples suggested by a library provided by the teacher, or an example formulated by the learner.&#13;
            &#13;
            The teacher level can create different libraries filled with example problems, according to the teacher's needs. The colaborator user can execute tasks related to library authoring, authorized by the teacher. The system provides an integration with Mathematical Computation systems, such as Maple and Scilab, aiming to offer the students computational resources to aid them on developing programs on the provided topics. Algebraic computation resources are provided by these systems, allowing to mix algebraic manipulation and numerical calculus, aiming to reduce errors caused by the use of a floating point system. This work is still in development. Critics, suggestions and comments are welcome, and should be sent to &lt;a href="mailto:angelica@uel.br"&gt; angelica@uel.br &lt;/a&gt;&#13;
        &lt;/p&gt;&#13;
        &lt;h2&gt;Team: &lt;/h2&gt;&#13;
        &lt;h2&gt;Coordinator:&lt;/h2&gt; &#13;
        &lt;p&gt;Maria Angélica de Oliveira Camargo Brunetto&lt;/p&gt;&#13;
        &lt;h2&gt;Scientific initiation students:&lt;/h2&gt; &#13;
        &lt;h2&gt; Previous years &lt;/h2&gt;&#13;
        &lt;p&gt;Claiton Oliveira &lt;/p&gt;&#13;
        &lt;p&gt;Cleberson Vidotte Costa &lt;/p&gt;&#13;
        &lt;p&gt;Douglas Terêncio do Vale &lt;/p&gt;&#13;
        &lt;p&gt;Marcelo Manzatto &lt;/p&gt;&#13;
        &lt;p&gt;Thalita Veronese  &lt;/p&gt;&#13;
        &lt;h2&gt; Current period &lt;/h2&gt;&#13;
        &lt;p&gt;Rafael Yul Arabori (2007/2008)&lt;/p&gt;</traducao>
  </sentenca>
  <sentenca xml:id="G_MSG_01">
    <traducao xml:lang="pt-br">Idioma</traducao>
    <traducao xml:lang="en-us">Language</traducao>
  </sentenca>
  <sentenca xml:id="G_MSG_02">
    <traducao xml:lang="pt-br">'Próximo &gt;&gt;'</traducao>
    <traducao xml:lang="en-us">'Next &gt;&gt;'</traducao>
  </sentenca>
  <sentenca xml:id="G_MSG_03">
    <traducao xml:lang="pt-br">Início</traducao>
    <traducao xml:lang="en-us">Start</traducao>
  </sentenca>
  <sentenca xml:id="G_MSG_04">
    <traducao xml:lang="pt-br">Calcular</traducao>
    <traducao xml:lang="en-us">Calculate</traducao>
  </sentenca>
  <sentenca xml:id="G_MSG_05">
    <traducao xml:lang="pt-br">Opções de execução do programa:</traducao>
    <traducao xml:lang="en-us">Options of program execution:</traducao>
  </sentenca>
  <sentenca xml:id="G_MSG_06">
    <traducao xml:lang="pt-br">Módulo de exemplos</traducao>
    <traducao xml:lang="en-us">Examples module</traducao>
  </sentenca>
  <sentenca xml:id="G_MSG_07">
    <traducao xml:lang="pt-br">Módulo de exercícios</traducao>
    <traducao xml:lang="en-us">Exercises module</traducao>
  </sentenca>
  <sentenca xml:id="G_MSG_08">
    <traducao xml:lang="pt-br">Módulo de exercícios - Opções de entrada de dados:</traducao>
    <traducao xml:lang="en-us">Exercises module - options of data input:</traducao>
  </sentenca>
  <sentenca xml:id="G_MSG_09">
    <traducao xml:lang="pt-br">Através de um arquivo de dados do usuário</traducao>
    <traducao xml:lang="en-us">Through an user's data file</traducao>
  </sentenca>
  <sentenca xml:id="G_MSG_10">
    <traducao xml:lang="pt-br">Módulo de exemplos - Opções de entrada de dados:</traducao>
    <traducao xml:lang="en-us">Examples module - options of data input:</traducao>
  </sentenca>
  <sentenca xml:id="G_MSG_11">
    <traducao xml:lang="pt-br">Através do teclado</traducao>
    <traducao xml:lang="en-us">Through the keyboard</traducao>
  </sentenca>
  <sentenca xml:id="G_MSG_12">
    <traducao xml:lang="pt-br">Entrada de dados via arquivo:</traducao>
    <traducao xml:lang="en-us">Input through a data file:</traducao>
  </sentenca>
  <sentenca xml:id="G_MSG_13">
    <traducao xml:lang="pt-br">Localização do arquivo de dados:</traducao>
    <traducao xml:lang="en-us">Localization of the data archive:</traducao>
  </sentenca>
  <sentenca xml:id="G_MSG_14">
    <traducao xml:lang="pt-br">Localização do arquivo de resposta:</traducao>
    <traducao xml:lang="en-us">Localization of the answer archive:</traducao>
  </sentenca>
  <sentenca xml:id="G_MSG_15">
    <traducao xml:lang="pt-br">Através de um biblioteca de problemas prontos</traducao>
    <traducao xml:lang="en-us">Through a library of ready problems</traducao>
  </sentenca>
  <sentenca xml:id="G_MSG_16">
    <traducao xml:lang="pt-br">Entrada de dados via biblioteca de problemas prontos</traducao>
    <traducao xml:lang="en-us">Data entry through a library of ready problems</traducao>
  </sentenca>
  <sentenca xml:id="G_MSG_17">
    <traducao xml:lang="pt-br">Clique em um link para selecionar um exemplo:</traducao>
    <traducao xml:lang="en-us">Click in one link to select an example:</traducao>
  </sentenca>
  <sentenca xml:id="G_MSG_18">
    <traducao xml:lang="pt-br"/>
    <traducao xml:lang="en-us"/>
  </sentenca>
  <sentenca xml:id="G_MSG_19">
    <traducao xml:lang="pt-br">Exibir algoritmo do método</traducao>
    <traducao xml:lang="en-us">Show the algorithm of the method</traducao>
  </sentenca>
  <sentenca xml:id="G_MSG_20">
    <traducao xml:lang="pt-br">Descrição do algoritmo</traducao>
    <traducao xml:lang="en-us">Algorithm's description</traducao>
  </sentenca>
  <sentenca xml:id="G_MSG_21">
    <traducao xml:lang="pt-br">&lt;&lt; Exemplo anterior</traducao>
    <traducao xml:lang="en-us">&lt;&lt; Previous example</traducao>
  </sentenca>
  <sentenca xml:id="G_MSG_22">
    <traducao xml:lang="pt-br">Menu de Exemplos</traducao>
    <traducao xml:lang="en-us">Menu of examples</traducao>
  </sentenca>
  <sentenca xml:id="G_MSG_23">
    <traducao xml:lang="pt-br">Próximo exemplo &gt;&gt;</traducao>
    <traducao xml:lang="en-us">Mext example &gt;&gt;</traducao>
  </sentenca>
  <sentenca xml:id="G_MSG_24">
    <traducao xml:lang="pt-br">Página Inicial</traducao>
    <traducao xml:lang="en-us">Initial page</traducao>
  </sentenca>
  <sentenca xml:id="G_MSG_25">
    <traducao xml:lang="pt-br">Como gerar seus arquivos? (Clique Aqui)</traducao>
    <traducao xml:lang="en-us">How to generate files? (Click here)</traducao>
  </sentenca>
  <sentenca xml:id="G_MSG_26">
    <traducao xml:lang="pt-br">Sobre este módulo</traducao>
    <traducao xml:lang="en-us">About this module</traducao>
  </sentenca>
  <sentenca xml:id="G_MSG_27">
    <traducao xml:lang="pt-br">
        &lt;font face=Arial&gt;
        &lt;p align=center&gt; &lt;font size=3&gt; &lt;b&gt; Sobre o módulo de exercícios &lt;/b&gt; &lt;/font&gt; &lt;/p&gt; 
        &lt;p&gt; &amp;nbsp&amp;nbsp&amp;nbsp
        No módulo de exercício, o aprendiz pode verificar se o programa implementado por ele fornece 
        as respostas corretas, submetendo um arquivo com os dados de entrada, um arquivo com os dados de resposta.
        Em cada categoria de problema, existe um link &lt;b&gt;Como gerar seus arquivos?&lt;/b&gt;, que detalha como os arquivos 
        de entrada de dados e de resposta devem ser gerados, seguindo o padrão reconhecido pelo programa. &lt;/p&gt;
        &lt;p&gt; &amp;nbsp&amp;nbsp&amp;nbsp
        Para cada problema, os arquivos são submetidos ao programa, que por sua vez extrai os dados necessários, 
        exibindo-os na tela. Então, o aprendiz pode executar os cálculos clicando em &lt;b&gt; Calcular &lt;/b&gt;. &lt;/p&gt;
        &lt;/font&gt;</traducao>
    <traducao xml:lang="en-us">
        &lt;font face=Arial&gt;
        &lt;p align=center&gt; &lt;font size=3&gt; &lt;b&gt; About the module of exercises &lt;/b&gt; &lt;/font&gt; &lt;/p&gt; 
        &lt;p&gt; &amp;nbsp&amp;nbsp&amp;nbsp
        In the exercise module, the apprentice can verify if the program implemented for it supplies the correct answers, submitting an archive with the entrance data, an archive with the answer data. In each category of problem, there is one link &lt;b&gt;How to generate your archives?&lt;/b&gt; , that details as the archives of data entry and of answer must be generated, following the recognized standard by the program. &lt;/p&gt;
        &lt;p&gt; &amp;nbsp&amp;nbsp&amp;nbsp
        For each problem, the archives are submitted to the program, that extracts the necessary data, showing them in the screen. Then, the apprentice can execute the method clicking in &lt;b&gt; Calculate &lt;/b&gt;. &lt;/p&gt;
        &lt;/font&gt;</traducao>
  </sentenca>
  <sentenca xml:id="G_MSG_28">
    <traducao xml:lang="pt-br">
        &lt;b&gt;Lista de funções reconhecidas pelo programa:&lt;br&gt;&lt;br&gt;&lt;/b&gt; &lt;br&gt;
        abs(num) -- Retorna o módulo de um número. Exemplo: abs(-5) = 5 &lt;br&gt;
        acos(num) -- Cosseno Inverso (arco cosseno) &lt;br&gt;
        acosh(num) -- Cosseno Hiperbólico Inverso &lt;br&gt;
        asin(num) -- Seno Inverso (arco seno) &lt;br&gt;
        asinh(num) -- Seno Hiperbólico Inverso &lt;br&gt;
        atan(num) -- Tangente Inversa (arco tangente) &lt;br&gt;
        atanh(num) -- Tangente hiperbólica inversa &lt;br&gt;
        cos(num) -- Cosseno &lt;br&gt;
        cosh(num) -- Cosseno hiperbólico &lt;br&gt;
        hypot(num1,num2) --  Retorna a raiz quadrada de (num1*num1 + num2*num2)  &lt;br&gt;
        log10(num) -- Logaritmo Base 10 &lt;br&gt;
        log(num) -- Logaritmo natural &lt;br&gt;
        potencia(base,expoente) -- Potência. Exemplo: potencia(3,4) = 81 &lt;br&gt;
        sin(num) -- Seno &lt;br&gt;
        sinh(num) -- Seno hiperbólico &lt;br&gt;
        sqrt(num) -- Raiz quadrada &lt;br&gt;
        tan(num) -- Tangente &lt;br&gt;
        tanh(num) -- Tangente hiperbólica &lt;br&gt; &lt;br&gt;
        Observe que o nome das funções está em letras &lt;b&gt;minúsculas&lt;/b&gt; e o valor de retorno está em &lt;b&gt;radianos&lt;/b&gt;, assim como deve ser o valor do parâmetro &lt;b&gt;num&lt;/b&gt;. &lt;br&gt;
        Caso queira entrar com algum valor em &lt;b&gt;graus&lt;/b&gt;, utilize a função deg2rad(num), onde num está em graus. Exemplo: Para cos 60&lt;sup&gt;o&lt;/sup&gt;, utilize cos(deg2rad(60)) &lt;br&gt;&lt;br&gt;
        &lt;b&gt;Lista de constantes reconhecidas pelo programa:&lt;br&gt;&lt;br&gt;&lt;/b&gt;
        E -- Valor do e neperiano. &lt;br&gt;
        PI -- Valor de pi &lt;br&gt;&lt;br&gt;
        Nos programas do NA-WEB, a única variável aceita é a variável 'x'. Exemplo de funções: &lt;br&gt; &lt;br&gt;
        3*potencia(x,2) = 3x&lt;sup&gt;2&lt;/sup&gt; &lt;br&gt;
        sin(abs(x-1)) = sen |x-1| &lt;br&gt;      
    </traducao>
    <traducao xml:lang="en-us">
        &lt;b&gt;List of functions recognized by the program:&lt;br&gt;&lt;br&gt;&lt;/b&gt; &lt;br&gt;
        abs(num) -- Absolute value. Example: abs(-5) = 5 &lt;br&gt;
        acos(num) -- Arc cosine &lt;br&gt;
        acosh(num) -- Inverse hyperbolic cosine &lt;br&gt;
        asin(num) -- Arc sine &lt;br&gt;
        asinh(num) -- Inverse hyperbolic sine &lt;br&gt;
        atan(num) -- Arc tangent &lt;br&gt;
        atanh(num) -- Inverse hyperbolic tangent &lt;br&gt;
        cos(num) -- Cosine &lt;br&gt;
        cosh(num) -- Hyperbolic cosine &lt;br&gt;
        hypot(num1,num2) --  Returns sqrt(num1*num1 + num2*num2)  &lt;br&gt;
        log10(num) -- Base-10 logarithm &lt;br&gt;
        log(num) -- Natural logarithm &lt;br&gt;
        potencia(base,expoente) -- Exponencial expression. Example: potencia(3,4) = 81 &lt;br&gt;
        sin(num) -- Sine &lt;br&gt;
        sinh(num) -- Hyperbolic sine &lt;br&gt;
        sqrt(num) -- Square root &lt;br&gt;
        tan(num) -- Tangent &lt;br&gt;
        tanh(num) -- Hyperbolic tangent &lt;br&gt; &lt;br&gt;
        Observe that the value of return of the functions are in &lt;b&gt;radians&lt;/b&gt;, as the value of &lt;b&gt;num&lt;/b&gt;. &lt;br&gt;
        If you want to use a value in &lt;b&gt;degrees&lt;/b&gt;, you can use the function deg2rad(num). Example: For cos 60&lt;sup&gt;o&lt;/sup&gt; use cos(deg2rad(60)) &lt;br&gt;&lt;br&gt;
        &lt;b&gt;List of constants recognized by the program:&lt;br&gt;&lt;br&gt;&lt;/b&gt;
        E -- Value of e (neperian). &lt;br&gt;
        PI -- Value of pi &lt;br&gt;&lt;br&gt;
        In the NA-WEB programs, the only accepted variable is the variable 'x'.  Example of functions: &lt;br&gt; &lt;br&gt;
        3*potencia(x,2) = 3x&lt;sup&gt;2&lt;/sup&gt; &lt;br&gt;
        sin(abs(x-1)) = sen |x-1| &lt;br&gt;
    </traducao>
  </sentenca>
  <sentenca xml:id="G_MSG_29">
    <traducao xml:lang="pt-br">&lt;font color=red&gt; Guia de referência de funções no ANA-WEB (Clique aqui) &lt;/font&gt;</traducao>
    <traducao xml:lang="en-us">&lt;font color=red&gt; ANA-WEB's function reference (Click here) &lt;/font&gt;</traducao>
  </sentenca>
  <sentenca xml:id="G_FORMULA_CHEBYSHEV">
    <traducao xml:lang="pt-br">&lt;font size=3&gt; x&lt;sub&gt;i&lt;/sub&gt; = (a + b) / 2 + (a - b) / 2 * cos ( &amp;#1083 (2i - 1) / 2n )&lt;/font&gt;</traducao>
    <traducao xml:lang="en-us">&lt;font size=3&gt; x&lt;sub&gt;i&lt;/sub&gt; = (a + b) / 2 + (a - b) / 2 * cos ( &amp;#1083 (2i - 1) / 2n )&lt;/font&gt;</traducao>
  </sentenca>
  <sentenca xml:id="G_PROXIMO_EXEMPLO">
    <traducao xml:lang="pt-br">Verifique a solução deste problema para os demais métodos: </traducao>
    <traducao xml:lang="en-us">Verify the solution to this problem for the other methods:</traducao>
  </sentenca>
  <sentenca xml:id="G_MODO_ALUNO">
    <traducao xml:lang="pt-br">Modo Aluno</traducao>
    <traducao xml:lang="en-us">Learner Mode</traducao>
  </sentenca>
  <sentenca xml:id="G_MODO_PROFESSOR">
    <traducao xml:lang="pt-br">Modo Autoria</traducao>
    <traducao xml:lang="en-us">Authoring Mode</traducao>
  </sentenca>
  <sentenca xml:id="G_INFORMA_MODO_NUMERICO">
    <traducao xml:lang="pt-br">Você está utilizando o Ambiente Numérico </traducao>
    <traducao xml:lang="en-us">You are using the Numerical Environment</traducao>
  </sentenca>
  <sentenca xml:id="G_TROCA_MODO_ALGEBRICO">
    <traducao xml:lang="pt-br">Acessar Ambiente Algébrico</traducao>
    <traducao xml:lang="en-us">Access Algebraic Environment</traducao>
  </sentenca>
  <sentenca xml:id="G_INFORMA_MODO_ALGEBRICO">
    <traducao xml:lang="pt-br">Você está utilizando o Ambiente Algébrico </traducao>
    <traducao xml:lang="en-us">You are using the Algebraic Environment</traducao>
  </sentenca>
  <sentenca xml:id="G_TROCA_MODO_NUMERICO">
    <traducao xml:lang="pt-br">Acessar Ambiente Numérico</traducao>
    <traducao xml:lang="en-us">Access Numerical Environment</traducao>
  </sentenca>
  <sentenca xml:id="G_AJUDA">
    <traducao xml:lang="pt-br">Ajuda</traducao>
    <traducao xml:lang="en-us">Help</traducao>
  </sentenca>
  <sentenca xml:id="FT_MSG_01">
    <traducao xml:lang="pt-br">ARITMÉTICA MATRICIAL</traducao>
    <traducao xml:lang="en-us">MATRICIAL ARITHMETIC</traducao>
  </sentenca>
  <sentenca xml:id="FT_MSG_02">
    <traducao xml:lang="pt-br">Determinante (por Gauss)</traducao>
    <traducao xml:lang="en-us">Determinant (by Gauss)</traducao>
  </sentenca>
  <sentenca xml:id="FT_MSG_03">
    <traducao xml:lang="pt-br">Inversa (por Gauss)</traducao>
    <traducao xml:lang="en-us">Inverse (by Gauss)</traducao>
  </sentenca>
  <sentenca xml:id="FT_MSG_041">
    <traducao xml:lang="pt-br">Decomposição de matrizes</traducao>
    <traducao xml:lang="en-us">Matrix decomposition</traducao>
  </sentenca>
  <sentenca xml:id="FT_MSG_042">
    <traducao xml:lang="pt-br">Matrizes definidas positivas</traducao>
    <traducao xml:lang="en-us">Definite positive matrices</traducao>
  </sentenca>
  <sentenca xml:id="FT_MSG_05">
    <traducao xml:lang="pt-br">Multiplicação</traducao>
    <traducao xml:lang="en-us">Multiplication</traducao>
  </sentenca>
  <sentenca xml:id="FT_MSG_06">
    <traducao xml:lang="pt-br">Soma</traducao>
    <traducao xml:lang="en-us">Sum</traducao>
  </sentenca>
  <sentenca xml:id="FT_MSG_07">
    <traducao xml:lang="pt-br">Transposta</traducao>
    <traducao xml:lang="en-us">Transpose</traducao>
  </sentenca>
  <sentenca xml:id="FT_MSG_08">
    <traducao xml:lang="pt-br">SISTEMAS DE EQUAÇÕES ALGÉBRICAS LINEARES</traducao>
    <traducao xml:lang="en-us">SYSTEM OF ALGEBRAIC LINEAR EQUATION</traducao>
  </sentenca>
  <sentenca xml:id="FT_MSG_09">
    <traducao xml:lang="pt-br">Métodos Diretos</traducao>
    <traducao xml:lang="en-us">Direct Methods</traducao>
  </sentenca>
  <sentenca xml:id="FT_MSG_10">
    <traducao xml:lang="pt-br">Eliminação de Gauss</traducao>
    <traducao xml:lang="en-us">Gauss Elimination</traducao>
  </sentenca>
  <sentenca xml:id="FT_MSG_11">
    <traducao xml:lang="pt-br">Sem pivoteamento</traducao>
    <traducao xml:lang="en-us">Without pivoting</traducao>
  </sentenca>
  <sentenca xml:id="FT_MSG_12">
    <traducao xml:lang="pt-br">Pivoteamento parcial</traducao>
    <traducao xml:lang="en-us">Parcial pivoting</traducao>
  </sentenca>
  <sentenca xml:id="FT_MSG_13">
    <traducao xml:lang="pt-br">Pivoteamento total</traducao>
    <traducao xml:lang="en-us">Maximal pivoting</traducao>
  </sentenca>
  <sentenca xml:id="FT_MSG_14">
    <traducao xml:lang="pt-br">Decomposição L.U.</traducao>
    <traducao xml:lang="en-us">L.U. Decompositio</traducao>
  </sentenca>
  <sentenca xml:id="FT_MSG_15">
    <traducao xml:lang="pt-br">Cholesky</traducao>
    <traducao xml:lang="en-us">Cholesky</traducao>
  </sentenca>
  <sentenca xml:id="FT_MSG_16">
    <traducao xml:lang="pt-br">Métodos Iterativos</traducao>
    <traducao xml:lang="en-us">Iterative Methods</traducao>
  </sentenca>
  <sentenca xml:id="FT_MSG_17">
    <traducao xml:lang="pt-br">Gauss-Seidel</traducao>
    <traducao xml:lang="en-us">Gauss-Seidel</traducao>
  </sentenca>
  <sentenca xml:id="FT_MSG_18">
    <traducao xml:lang="pt-br">Jacobi</traducao>
    <traducao xml:lang="en-us">Jacobi</traducao>
  </sentenca>
  <sentenca xml:id="FT_MSG_19">
    <traducao xml:lang="pt-br">MÉTODOS DE INTERPOLAÇÃO </traducao>
    <traducao xml:lang="en-us">INTERPOLATION METHODS</traducao>
  </sentenca>
  <sentenca xml:id="FT_MSG_20">
    <traducao xml:lang="pt-br">Lagrange</traducao>
    <traducao xml:lang="en-us">Lagrange</traducao>
  </sentenca>
  <sentenca xml:id="FT_MSG_21">
    <traducao xml:lang="pt-br">Newton</traducao>
    <traducao xml:lang="en-us">Newton</traducao>
  </sentenca>
  <sentenca xml:id="FT_MSG_22">
    <traducao xml:lang="pt-br">Splines cúbicos</traducao>
    <traducao xml:lang="en-us">Cubic splines</traducao>
  </sentenca>
  <sentenca xml:id="FT_MSG_23">
    <traducao xml:lang="pt-br">AJUSTE DE DADOS</traducao>
    <traducao xml:lang="en-us">DATA FITTING</traducao>
  </sentenca>
  <sentenca xml:id="FT_MSG_24">
    <traducao xml:lang="pt-br">Mínimos quadrados</traducao>
    <traducao xml:lang="en-us">Least-squares approximation</traducao>
  </sentenca>
  <sentenca xml:id="FT_MSG_25">
    <traducao xml:lang="pt-br">Mínimos quadrados com polinômios ortogonais (Finalizando)</traducao>
    <traducao xml:lang="en-us">Mínimos quadrados com polinômios ortogonais (Finalizando)</traducao>
  </sentenca>
  <sentenca xml:id="FT_MSG_26">
    <traducao xml:lang="pt-br">RESOLUÇÃO DE EQUAÇÕES NÃO-LINEARES</traducao>
    <traducao xml:lang="en-us">NONLINEAR EQUATION SOLVING</traducao>
  </sentenca>
  <sentenca xml:id="FT_MSG_27">
    <traducao xml:lang="pt-br">Método da Bissecção</traducao>
    <traducao xml:lang="en-us">Bisection method</traducao>
  </sentenca>
  <sentenca xml:id="FT_MSG_28">
    <traducao xml:lang="pt-br">Método da Secante</traducao>
    <traducao xml:lang="en-us">Secant method</traducao>
  </sentenca>
  <sentenca xml:id="FT_MSG_29">
    <traducao xml:lang="pt-br">Método de Newton</traducao>
    <traducao xml:lang="en-us">Newton's method</traducao>
  </sentenca>
  <sentenca xml:id="FT_MSG_30">
    <traducao xml:lang="pt-br">SISTEMAS DE EQUAÇÕES ALGÉBRICAS NÃO-LINEARES</traducao>
    <traducao xml:lang="en-us">SYSTEM OF NONLINEAR ALGEBRAIC EQUATION</traducao>
  </sentenca>
  <sentenca xml:id="FT_MSG_31">
    <traducao xml:lang="pt-br">Método de Newton</traducao>
    <traducao xml:lang="en-us">Newton's method</traducao>
  </sentenca>
  <sentenca xml:id="FT_MSG_32">
    <traducao xml:lang="pt-br">INTEGRAIS E DERIVADAS</traducao>
    <traducao xml:lang="en-us">INTEGRATION AND DERIVATIVES</traducao>
  </sentenca>
  <sentenca xml:id="FT_MSG_33">
    <traducao xml:lang="pt-br">Integração numérica</traducao>
    <traducao xml:lang="en-us">Numerical integration</traducao>
  </sentenca>
  <sentenca xml:id="FT_MSG_34">
    <traducao xml:lang="pt-br">Método de Richardson</traducao>
    <traducao xml:lang="en-us">Richardson's method</traducao>
  </sentenca>
  <sentenca xml:id="FT_MSG_35">
    <traducao xml:lang="pt-br">Método de Romberg</traducao>
    <traducao xml:lang="en-us">Romberg's method</traducao>
  </sentenca>
  <sentenca xml:id="FT_MSG_36">
    <traducao xml:lang="pt-br">Método de Simpson</traducao>
    <traducao xml:lang="en-us">Simpson's method</traducao>
  </sentenca>
  <sentenca xml:id="FT_MSG_37">
    <traducao xml:lang="pt-br">Método do trapézio</traducao>
    <traducao xml:lang="en-us">Trapezoidal method</traducao>
  </sentenca>
  <sentenca xml:id="FT_MSG_38">
    <traducao xml:lang="pt-br">EQUAÇÕES DIFERENCIAIS ORIDINÁRIAS (em construção)</traducao>
    <traducao xml:lang="en-us">ORDINARY DIFFERENTIAL EQUATIONS (Finishing)</traducao>
  </sentenca>
  <sentenca xml:id="FT_MSG_39">
    <traducao xml:lang="pt-br">Derivação numérica</traducao>
    <traducao xml:lang="en-us">Numerical derivative</traducao>
  </sentenca>
  <sentenca xml:id="FT_MSG_40">
    <traducao xml:lang="pt-br">Diferença central</traducao>
    <traducao xml:lang="en-us">Central diference</traducao>
  </sentenca>
  <sentenca xml:id="FT_MSG_41">
    <traducao xml:lang="pt-br">ARITMÉTICA DE PONTO FLUTUANTE</traducao>
    <traducao xml:lang="en-us">FLOATING POINT ARITHMETIC</traducao>
  </sentenca>
  <sentenca xml:id="FT_MSG_42">
    <traducao xml:lang="pt-br">Sistema de ponto flutuante</traducao>
    <traducao xml:lang="en-us">Floating point system</traducao>
  </sentenca>
  <sentenca xml:id="FT_MSG_43">
    <traducao xml:lang="pt-br">Soma</traducao>
    <traducao xml:lang="en-us">Sum</traducao>
  </sentenca>
  <sentenca xml:id="FT_MSG_44">
    <traducao xml:lang="pt-br">Multiplicação</traducao>
    <traducao xml:lang="en-us">Multiplication</traducao>
  </sentenca>
  <sentenca xml:id="FT_MSG_45">
    <traducao xml:lang="pt-br">Divisão</traducao>
    <traducao xml:lang="en-us">Division</traducao>
  </sentenca>
  <sentenca xml:id="FT_MSG_46">
    <traducao xml:lang="pt-br">Subtração</traducao>
    <traducao xml:lang="en-us">Subtraction</traducao>
  </sentenca>
  <sentenca xml:id="FT_MSG_47">
    <traducao xml:lang="pt-br">Biblioteca de problemas</traducao>
    <traducao xml:lang="en-us">Library of ready problems</traducao>
  </sentenca>
  <sentenca xml:id="FT_MSG_48">
    <traducao xml:lang="pt-br">Resolução de problemas</traducao>
    <traducao xml:lang="en-us">Problems resolution</traducao>
  </sentenca>
  <sentenca xml:id="AJDADOS_MSG_01">
    <traducao xml:lang="pt-br">Método dos mínimos quadrados</traducao>
    <traducao xml:lang="en-us">Least-squares approximation</traducao>
  </sentenca>
  <sentenca xml:id="AJDADOS_MSG_02">
    <traducao xml:lang="pt-br">Ajuste de Dados</traducao>
    <traducao xml:lang="en-us">Data Fitting</traducao>
  </sentenca>
  <sentenca xml:id="AJDADOS_MSG_03">
    <traducao xml:lang="pt-br">Método dos mínimos quadrados</traducao>
    <traducao xml:lang="en-us">Least-squares approximation</traducao>
  </sentenca>
  <sentenca xml:id="AJDADOS_MSG_04">
    <traducao xml:lang="pt-br">Selecione uma opção para entrada de dados:</traducao>
    <traducao xml:lang="en-us">Select one option for data entry:</traducao>
  </sentenca>
  <sentenca xml:id="AJDADOS_MSG_05">
    <traducao xml:lang="pt-br">Caso discreto (através de um conjunto de pontos)</traducao>
    <traducao xml:lang="en-us">Discrete case (through a set of points)</traducao>
  </sentenca>
  <sentenca xml:id="AJDADOS_MSG_06">
    <traducao xml:lang="pt-br">Caso contínuo (através de uma função e um intervalo)</traducao>
    <traducao xml:lang="en-us">Discrete case (through a function and an interval)</traducao>
  </sentenca>
  <sentenca xml:id="AJDADOS_MSG_07">
    <traducao xml:lang="pt-br">Digite o número de pontos que serão dados como entrada: </traducao>
    <traducao xml:lang="en-us">Type the number of points:</traducao>
  </sentenca>
  <sentenca xml:id="AJDADOS_MSG_08">
    <traducao xml:lang="pt-br">Digite o grau do polinômio que será dado como entrada: </traducao>
    <traducao xml:lang="en-us">Type the degree of the polynomial: </traducao>
  </sentenca>
  <sentenca xml:id="AJDADOS_MSG_09">
    <traducao xml:lang="pt-br">Digite as coordenadas x e f(x) dos pontos: </traducao>
    <traducao xml:lang="en-us">Type the coordinates x and f(x) of the points:</traducao>
  </sentenca>
  <sentenca xml:id="AJDADOS_MSG_10">
    <traducao xml:lang="pt-br">Digite a função: </traducao>
    <traducao xml:lang="en-us">Type the function:</traducao>
  </sentenca>
  <sentenca xml:id="AJDADOS_MSG_11">
    <traducao xml:lang="pt-br">Digite o intervalo em que a função será aproximada: </traducao>
    <traducao xml:lang="en-us">Type the interval where the function will be approached:</traducao>
  </sentenca>
  <sentenca xml:id="AJDADOS_MSG_12">
    <traducao xml:lang="pt-br">Informe o grau g(x) do polinômio aproximador, tal que g(x) &lt; </traducao>
    <traducao xml:lang="en-us">Inform the degree g(x) of the least-squares polynomial, such that g(x) &lt;</traducao>
  </sentenca>
  <sentenca xml:id="AJDADOS_MSG_12a">
    <traducao xml:lang="pt-br">Informe o grau g(x) do polinômio aproximador </traducao>
    <traducao xml:lang="en-us">Inform the degree g(x) of the least-squares polynomial</traducao>
  </sentenca>
  <sentenca xml:id="AJDADOS_MSG_13">
    <traducao xml:lang="pt-br">Resposta retirada do arquivo:</traducao>
    <traducao xml:lang="en-us">Answer obtained from the file:</traducao>
  </sentenca>
  <sentenca xml:id="AJDADOS_MSG_14">
    <traducao xml:lang="pt-br">Polinômio aproximador de grau </traducao>
    <traducao xml:lang="en-us">Polynomial of degree </traducao>
  </sentenca>
  <sentenca xml:id="AJDADOS_MSG_15">
    <traducao xml:lang="pt-br"> usando método dos Mínimos Quadrados:</traducao>
    <traducao xml:lang="en-us"> using least-squares approximation method:</traducao>
  </sentenca>
  <sentenca xml:id="AJDADOS_MSG_16">
    <traducao xml:lang="pt-br">Coordenadas dos pontos dados:</traducao>
    <traducao xml:lang="en-us">Coordinates of the given points:</traducao>
  </sentenca>
  <sentenca xml:id="AJDADOS_MSG_17">
    <traducao xml:lang="pt-br">Resposta obtida do programa:</traducao>
    <traducao xml:lang="en-us">Answer obtained:</traducao>
  </sentenca>
  <sentenca xml:id="AJDADOS_MSG_18">
    <traducao xml:lang="pt-br">Função dada no intervalo </traducao>
    <traducao xml:lang="en-us">Function given in the interval </traducao>
  </sentenca>
  <sentenca xml:id="AJDADOS_MSG_19">
    <traducao xml:lang="pt-br">Resposta obtida do arquivo:</traducao>
    <traducao xml:lang="en-us">Answer obtained from file:</traducao>
  </sentenca>
  <sentenca xml:id="AJDADOS_MSG_20">
    <traducao xml:lang="pt-br">pontos</traducao>
    <traducao xml:lang="en-us">poitns</traducao>
  </sentenca>
  <sentenca xml:id="AJDADOS_MSG_21">
    <traducao xml:lang="pt-br">Função dada: </traducao>
    <traducao xml:lang="en-us">Given function: </traducao>
  </sentenca>
  <sentenca xml:id="AJDADOS_MSG_22">
    <traducao xml:lang="pt-br">'Escolher outro grau para o polinômio'</traducao>
    <traducao xml:lang="en-us">'Choose another degree for the polynom'</traducao>
  </sentenca>
  <sentenca xml:id="AJDADOS_ALGORITMO">
    <traducao xml:lang="pt-br">
        &lt;b&gt;Variáveis: &lt;/b&gt; &lt;br&gt;&lt;br&gt; 
        Auxiliares: &lt;br&gt;
        i, j, k, l, m, cont (contadores), vff, mxt, c, v, vetor_resposta (vetores), A, mxf (matrizes), f, fa, fb, delta, sum, aprox aux, maior, indice, cont, diferenca, xo &lt;br&gt;&lt;br&gt;
        De entrada: &lt;br&gt;
        Caso discreto &lt;br&gt;
        pontos (número de pontos), vetx, vetf (vetores), grau (grau do polinômio aproximador) &lt;br&gt;
        Caso contínuo &lt;br&gt;
        deg (grau do polinômio de entrada), int1, int2 (intervalo em que o polinômio será aproximado), coef (vetor dos coeficientes do polinômio), grau (grau do polinômio aproximador) 
        &lt;br&gt;&lt;br&gt;
        De saída: &lt;br&gt;
        coeficientes_polinômio (coeficientes do polinômio aproximador)&lt;br&gt;&lt;br&gt;
        &lt;b&gt;Algoritmo: &lt;/b&gt; &lt;br&gt;&lt;br&gt; 
        função evalf(x,deg,coef) &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; f := 0 &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; para i de 0 a deg-1 faça &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; f := f + coef&lt;sub&gt;&lt;font size=2&gt;i&lt;/font&gt;&lt;/sub&gt; * x&lt;sup&gt;deg-i&lt;/sup&gt; &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim para &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; f := f + coef&lt;sub&gt;&lt;font size=2&gt;deg&lt;/font&gt;&lt;/sub&gt; &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; retorna f &lt;br&gt;
        fim função &lt;br&gt; &lt;br&gt;
        função trapézio (a,b,vn,coef,deg)  &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fa := evalf(a,deg,coef) &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fb := evalf(b,deg,coef) &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; delta := (b-a) / vn &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; para i de 0 a vn-2 faça &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; v&lt;sub&gt;&lt;font size=2&gt;i&lt;/font&gt;&lt;/sub&gt; := evalf(a+((i+1)*delta),deg,coef) &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim para &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; sum := 0 &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; sum := fa+fb &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; para i de 0 a vn-2 faça &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; sum := sum + (2*v&lt;sub&gt;&lt;font size=2&gt;i&lt;/font&gt;&lt;/sub&gt;) &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim para &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; aprox := ( (b-a) / (2*vn) ) * sum &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; retorna aprox &lt;br&gt;
        fim função &lt;br&gt; &lt;br&gt;
        função triangularização (A,dim)  &lt;br&gt; 
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; para k de 0 a dim-2 faça &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; para i de k+1 a dim-1 faça &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; se A&lt;sub&gt;&lt;font size=2&gt;k,k&lt;/font&gt;&lt;/sub&gt; = 0 então //pivô se anula &lt;br&gt; 
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; maior := módulo(A&lt;sub&gt;&lt;font size=2&gt;k,k&lt;/font&gt;&lt;/sub&gt;) &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; para cont de k+1 a dim-1 faça &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; //encontra elemento de maior valor absoluto na k-ésima coluna &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; se módulo(A&lt;sub&gt;&lt;font size=2&gt;cont,k&lt;/font&gt;&lt;/sub&gt;) &gt; maior então &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; maior := módulo(A&lt;sub&gt;&lt;font size=2&gt;cont,k&lt;/font&gt;&lt;/sub&gt;) &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; indice := cont &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim se &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim para &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; para l de 0 a dim faça //troca de linha &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; aux2 := A&lt;sub&gt;&lt;font size=2&gt;k,l&lt;/font&gt;&lt;/sub&gt; &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; A&lt;sub&gt;&lt;font size=2&gt;k,l&lt;/font&gt;&lt;/sub&gt; := A&lt;sub&gt;&lt;font size=2&gt;indice,l&lt;/font&gt;&lt;/sub&gt; &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; A&lt;sub&gt;&lt;font size=2&gt;indice,l&lt;/font&gt;&lt;/sub&gt; := aux2 &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim para &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim se &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; M&lt;sub&gt;&lt;font size=2&gt;i,k&lt;/font&gt;&lt;/sub&gt; := M&lt;sub&gt;&lt;font size=2&gt;i,k&lt;/font&gt;&lt;/sub&gt; - A&lt;sub&gt;&lt;font size=2&gt;i,k&lt;/font&gt;&lt;/sub&gt;/A&lt;sub&gt;&lt;font size=2&gt;k,k&lt;/font&gt;&lt;/sub&gt; &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; para j de 0 a dim faça &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; A&lt;sub&gt;&lt;font size=2&gt;i,j&lt;/font&gt;&lt;/sub&gt; := A&lt;sub&gt;&lt;font size=2&gt;i,j&lt;/font&gt;&lt;/sub&gt; + M&lt;sub&gt;&lt;font size=2&gt;i,k&lt;/font&gt;&lt;/sub&gt; * A&lt;sub&gt;&lt;font size=2&gt;k,j&lt;/font&gt;&lt;/sub&gt; &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim para &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim para &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim para &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; retorna A &lt;br&gt;
        fim função &lt;br&gt; &lt;br&gt;
        função retrosubstituição (B,dim)  &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; se B&lt;sub&gt;&lt;font size=2&gt;dim-1,dim-1&lt;/font&gt;&lt;/sub&gt; = 0 então &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; se B&lt;sub&gt;&lt;font size=2&gt;dim-1,dim&lt;/font&gt;&lt;/sub&gt; = 0  então // sistema tem infinitas soluções &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; vetor_resposta&lt;sub&gt;&lt;font size=2&gt;dim-1&lt;/font&gt;&lt;/sub&gt; := 1 &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; para k de dim-2 a 0 faça &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; vetor_resposta&lt;sub&gt;&lt;font size=2&gt;k&lt;/font&gt;&lt;/sub&gt; := B&lt;sub&gt;&lt;font size=2&gt;k,dim&lt;/font&gt;&lt;/sub&gt; &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; para i de k+1 a dim-1 faça &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; vetor_resposta&lt;sub&gt;&lt;font size=2&gt;k&lt;/font&gt;&lt;/sub&gt; := vetor_resposta&lt;sub&gt;&lt;font size=2&gt;k&lt;/font&gt;&lt;/sub&gt; - B&lt;sub&gt;&lt;font size=2&gt;k,i&lt;/font&gt;&lt;/sub&gt; * vetor_resposta&lt;sub&gt;&lt;font size=2&gt;i&lt;/font&gt;&lt;/sub&gt; &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim para &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; vetor_resposta&lt;sub&gt;&lt;font size=2&gt;k&lt;/font&gt;&lt;/sub&gt; := vetor_resposta&lt;sub&gt;&lt;font size=2&gt;k&lt;/font&gt;&lt;/sub&gt; / B&lt;sub&gt;&lt;font size=2&gt;k,k&lt;/font&gt;&lt;/sub&gt; &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim para &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; senão // sistema não possui solução &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; parar o método &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim se   &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; senão // sistema possui solução única &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; vetor_resposta&lt;sub&gt;&lt;font size=2&gt;dim-1&lt;/font&gt;&lt;/sub&gt; := B&lt;sub&gt;&lt;font size=2&gt;dim-1,dim&lt;/font&gt;&lt;/sub&gt; / B&lt;sub&gt;&lt;font size=2&gt;dim-1,dim-1&lt;/font&gt;&lt;/sub&gt; &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; para k de dim-2 a 0 faça &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; vetor_resposta&lt;sub&gt;&lt;font size=2&gt;k&lt;/font&gt;&lt;/sub&gt; := B&lt;sub&gt;&lt;font size=2&gt;k,dim&lt;/font&gt;&lt;/sub&gt; &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; para i de k+1 a dim-1 faça &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; vetor_resposta&lt;sub&gt;&lt;font size=2&gt;k&lt;/font&gt;&lt;/sub&gt; := vetor_resposta&lt;sub&gt;&lt;font size=2&gt;k&lt;/font&gt;&lt;/sub&gt; - B&lt;sub&gt;&lt;font size=2&gt;k,i&lt;/font&gt;&lt;/sub&gt; * vetor_resposta&lt;sub&gt;&lt;font size=2&gt;i&lt;/font&gt;&lt;/sub&gt; &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim para &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; vetor_resposta&lt;sub&gt;&lt;font size=2&gt;k&lt;/font&gt;&lt;/sub&gt; := vetor_resposta&lt;sub&gt;&lt;font size=2&gt;k&lt;/font&gt;&lt;/sub&gt; / B&lt;sub&gt;&lt;font size=2&gt;k,k&lt;/font&gt;&lt;/sub&gt; &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim para &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim se &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; retorna vetor_resposta &lt;br&gt;
        fim função &lt;br&gt; &lt;br&gt;    
        função mínimos_quadrados(vetx,vetf,pontos,grau) &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; para i de 0 a grau faça &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; para j de 0 a pontos-1 faça &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; mx&lt;sub&gt;&lt;font size=2&gt;j,i&lt;/font&gt;&lt;/sub&gt; := vetx&lt;sub&gt;&lt;font size=2&gt;j&lt;/font&gt;&lt;/sub&gt;&lt;sup&gt;i&lt;/sup&gt; &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; mxt&lt;sub&gt;&lt;font size=2&gt;i,j&lt;/font&gt;&lt;/sub&gt; := vetx&lt;sub&gt;&lt;font size=2&gt;j&lt;/font&gt;&lt;/sub&gt;&lt;sup&gt;i&lt;/sup&gt; &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim para &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim para &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; para k de 0 a grau faça &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; para l de 0 a grau faça &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; mxf&lt;sub&gt;&lt;font size=2&gt;k,l&lt;/font&gt;&lt;/sub&gt; := 0 &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; vff&lt;sub&gt;&lt;font size=2&gt;k&lt;/font&gt;&lt;/sub&gt; := 0 &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; para m de 0 a pontos-1 faça &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; mxf&lt;sub&gt;&lt;font size=2&gt;k,l&lt;/font&gt;&lt;/sub&gt; := mxf&lt;sub&gt;&lt;font size=2&gt;k,l&lt;/font&gt;&lt;/sub&gt; + (mxt&lt;sub&gt;&lt;font size=2&gt;k,m&lt;/font&gt;&lt;/sub&gt;*mx&lt;sub&gt;&lt;font size=2&gt;m,l&lt;/font&gt;&lt;/sub&gt;) &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; vff&lt;sub&gt;&lt;font size=2&gt;k&lt;/font&gt;&lt;/sub&gt; := vff&lt;sub&gt;&lt;font size=2&gt;k&lt;/font&gt;&lt;/sub&gt; + (mxt&lt;sub&gt;&lt;font size=2&gt;k,m&lt;/font&gt;&lt;/sub&gt;*vetf&lt;sub&gt;&lt;font size=2&gt;m&lt;/font&gt;&lt;/sub&gt;) &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim para &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim para &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim para &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; para n de 0 a grau faça &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; mxf&lt;sub&gt;&lt;font size=2&gt;n,grau+1&lt;/font&gt;&lt;/sub&gt; := vff&lt;sub&gt;&lt;font size=2&gt;n&lt;/font&gt;&lt;/sub&gt; &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim para &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; coeficientes_polinômio := retrosubstituição(triangularização(mxf,grau+1),grau+1) &lt;br&gt;
        fim função &lt;br&gt; &lt;br&gt;
        função mínimos_quadrados_cont(deg,grau,coef,int1,int2) &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; para i de 0 a grau faça &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; A&lt;sub&gt;&lt;font size=2&gt;i,grau+1&lt;/font&gt;&lt;/sub&gt; := trapézio(int1,int2,500,coef,deg+i) &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; para j de 0 a grau faça &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; c&lt;sub&gt;&lt;font size=2&gt;0&lt;/font&gt;&lt;/sub&gt; := 1 &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; para k de 1 a i+j faça &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; c&lt;sub&gt;&lt;font size=2&gt;k&lt;/font&gt;&lt;/sub&gt; := 0 &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim para &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; A&lt;sub&gt;&lt;font size=2&gt;i,j&lt;/font&gt;&lt;/sub&gt; = trapézio(int1,int2,10,c,i + j) &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim para &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim para &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; coeficientes_polinômio := retrosubstituição(triangularização(A,grau+1),grau+1) &lt;br&gt;
        fim função &lt;br&gt; &lt;br&gt;
        se entrada de dados = caso discreto então &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; minimos_quadrados(vetx,vetf,pontos,grau) &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; retorna coeficientes_polinômio &lt;br&gt;
        fim se &lt;br&gt;
        senão se entrada de dados = caso contínuo então &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; minimos_quadrados_cont(deg,grau,coef,int1,int2) &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; retorna coeficientes_polinômio &lt;br&gt;
        fim senão  </traducao>
    <traducao xml:lang="en-us"/>
  </sentenca>
  <sentenca xml:id="AJDADOS_AJUDA">
    <traducao xml:lang="pt-br">
        &lt;ul&gt;
        &lt;li&gt;Os arquivos devem estar no formato .txt.&lt;/li&gt; &lt;br&gt;
        &lt;li&gt;Cada linha deve conter apenas &lt;b&gt;um&lt;/b&gt; valor, na seguinte ordem: &lt;/li&gt; &lt;br&gt;
        &lt;li&gt; &lt;b&gt; Arquivo de dados &lt;/b&gt;
        &lt;br&gt;
        &lt;br&gt; 1ª linha: '0' (Zero) para o caso discreto (pontos) e 1 para caso contínuo (uma função). &lt;br&gt;
        &lt;br&gt; 2ª linha: número de pontos para o caso discreto, ou própria a função (no &lt;a href=javascript:winopen('funcoesphp.php')&gt;formato&lt;/a&gt; reconhecido pelo programa) para o caso contínuo. &lt;br&gt;
        &lt;br&gt; Para o caso discreto: A partir da 3ª linha, informar os valores dos pontos x e f(x), um par de pontos por linha, da seguinte forma: x;f(x). &lt;br&gt;
        &lt;br&gt; Para o caso contínuo: Na 3ª linha, inserir o intervalo em que se deseja aproximar a função, no seguinte formato: a&lt;font size=4&gt;&lt;b&gt;;&lt;/b&gt;&lt;/font&gt;b. &lt;br&gt;
        &lt;br&gt; Na última linha, em todos os casos, inserir o grau do polinômio aproximador. &lt;br&gt; &lt;br&gt;
        &lt;li&gt; &lt;b&gt; Arquivo de resposta &lt;/b&gt;
        &lt;br&gt;
        &lt;br&gt; A partir da 1ª linha: coeficientes do polinômio interpolador, a partir do coeficiente que acompanha a variável de maior grau. &lt;br&gt;
        &lt;/ul&gt;
    </traducao>
    <traducao xml:lang="en-us"/>
  </sentenca>
  <sentenca xml:id="AJDADOS_EXE_01">
    <traducao xml:lang="pt-br">Caso discreto - 6 pontos e aproximação por uma reta</traducao>
    <traducao xml:lang="en-us"/>
  </sentenca>
  <sentenca xml:id="AJDADOS_EXE_02">
    <traducao xml:lang="pt-br">Caso discreto - 5 pontos e aproximação por uma reta</traducao>
    <traducao xml:lang="en-us"/>
  </sentenca>
  <sentenca xml:id="CHOLESKY_MSG_01">
    <traducao xml:lang="pt-br">Cholesky</traducao>
    <traducao xml:lang="en-us">Cholesky</traducao>
  </sentenca>
  <sentenca xml:id="CHOLESKY_MSG_02">
    <traducao xml:lang="pt-br">Sistemas de Equações Algébricas Lineares</traducao>
    <traducao xml:lang="en-us">System of Linear Algebraic Equations</traducao>
  </sentenca>
  <sentenca xml:id="CHOLESKY_MSG_03">
    <traducao xml:lang="pt-br">Cholesky</traducao>
    <traducao xml:lang="en-us">Cholesky</traducao>
  </sentenca>
  <sentenca xml:id="CHOLESKY_MSG_04">
    <traducao xml:lang="pt-br">Dimensão (número de variáveis): </traducao>
    <traducao xml:lang="en-us">Dimension (number of variables):</traducao>
  </sentenca>
  <sentenca xml:id="CHOLESKY_MSG_05">
    <traducao xml:lang="pt-br">Sistema</traducao>
    <traducao xml:lang="en-us">Sistema</traducao>
  </sentenca>
  <sentenca xml:id="CHOLESKY_MSG_06">
    <traducao xml:lang="pt-br">Solução retirada do arquivo: </traducao>
    <traducao xml:lang="en-us">Solution obtained from file:</traducao>
  </sentenca>
  <sentenca xml:id="CHOLESKY_MSG_07">
    <traducao xml:lang="pt-br">Matriz A</traducao>
    <traducao xml:lang="en-us">Matrix A</traducao>
  </sentenca>
  <sentenca xml:id="CHOLESKY_MSG_08">
    <traducao xml:lang="pt-br">Matriz U</traducao>
    <traducao xml:lang="en-us">Matrix U</traducao>
  </sentenca>
  <sentenca xml:id="CHOLESKY_MSG_09">
    <traducao xml:lang="pt-br">Matriz U&lt;sub&gt;t&lt;/sub&gt;</traducao>
    <traducao xml:lang="en-us">Matrix U&lt;sub&gt;t&lt;/sub&gt;</traducao>
  </sentenca>
  <sentenca xml:id="CHOLESKY_MSG_10">
    <traducao xml:lang="pt-br">A matriz não é simétrica.</traducao>
    <traducao xml:lang="en-us">The matrix is not symetric</traducao>
  </sentenca>
  <sentenca xml:id="CHOLESKY_MSG_11">
    <traducao xml:lang="pt-br">Solução obtida do programa: </traducao>
    <traducao xml:lang="en-us">Solution obtained from the program: </traducao>
  </sentenca>
  <sentenca xml:id="CHOLESKY_MSG_12">
    <traducao xml:lang="pt-br">Solução obtida do arquivo: </traducao>
    <traducao xml:lang="en-us">Solution obtained from file: </traducao>
  </sentenca>
  <sentenca xml:id="CHOLESKY_MSG_13">
    <traducao xml:lang="pt-br">O método não se aplica pois a matriz de coeficientes não é definida positiva. </traducao>
    <traducao xml:lang="en-us">The method cannot be applied, the matrix of coefficients is not definite positive</traducao>
  </sentenca>
  <sentenca xml:id="CHOLESKY_ALGORITMO">
    <traducao xml:lang="pt-br">
        &lt;b&gt;Variáveis: &lt;/b&gt; &lt;br&gt;&lt;br&gt; 
        Auxiliares: &lt;br&gt;
        h, i, j, k, p (contadores), U, Ut, (matrizes), VetY (vetor), somatmp, soma&lt;br&gt;&lt;br&gt;
        De entrada: &lt;br&gt;
        dim (dimensão da matriz), A e T (matriz e vetor, para o sistema A x = T)  &lt;br&gt;&lt;br&gt;
        De saída: &lt;br&gt;
        VetX (vetor - quando há solução)&lt;br&gt;&lt;br&gt;
        &lt;b&gt;Algoritmo: &lt;/b&gt; &lt;br&gt;&lt;br&gt; 
        função transposta(A,dim) &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; para i de 0 a dim-1 faça &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; para j de 0 a dim-1 faça &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; Ut&lt;sub&gt;&lt;font size=2&gt;i,j&lt;/font&gt;&lt;/sub&gt; := A&lt;sub&gt;&lt;font size=2&gt;j,i&lt;/font&gt;&lt;/sub&gt; &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim para &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim para &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; retorna Ut &lt;br&gt;
        fim função &lt;br&gt; &lt;br&gt;
        função retrosubstituição(B,dim) &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; VetX&lt;sub&gt;&lt;font size=2&gt;dim-1&lt;/font&gt;&lt;/sub&gt; := B&lt;sub&gt;&lt;font size=2&gt;dim-1,dim&lt;/font&gt;&lt;/sub&gt;/B&lt;sub&gt;&lt;font size=2&gt;dim-1,dim-1&lt;/font&gt;&lt;/sub&gt; &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; para k de dim-2 a 0 faça &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; VetX&lt;sub&gt;&lt;font size=2&gt;k&lt;/font&gt;&lt;/sub&gt; := B&lt;sub&gt;&lt;font size=2&gt;k,dim&lt;/font&gt;&lt;/sub&gt; &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; para i de k+1 a dim-1 faça &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; VetX&lt;sub&gt;&lt;font size=2&gt;k&lt;/font&gt;&lt;/sub&gt; := VetX&lt;sub&gt;&lt;font size=2&gt;k&lt;/font&gt;&lt;/sub&gt; - B&lt;sub&gt;&lt;font size=2&gt;k,i&lt;/font&gt;&lt;/sub&gt; * VetX&lt;sub&gt;&lt;font size=2&gt;i&lt;/font&gt;&lt;/sub&gt; &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim para &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; VetX&lt;sub&gt;&lt;font size=2&gt;k&lt;/font&gt;&lt;/sub&gt; := VetX&lt;sub&gt;&lt;font size=2&gt;k&lt;/font&gt;&lt;/sub&gt; / B&lt;sub&gt;&lt;font size=2&gt;k,k&lt;/font&gt;&lt;/sub&gt; &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim para &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; retorna VetX &lt;br&gt;
        fim função &lt;br&gt; &lt;br&gt;
        funçao forwardsubstituição(f,dim)  &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; VetY&lt;sub&gt;&lt;font size=2&gt;0&lt;/font&gt;&lt;/sub&gt; := f&lt;sub&gt;&lt;font size=2&gt;0,dim&lt;/font&gt;&lt;/sub&gt;/f&lt;sub&gt;&lt;font size=2&gt;0,0&lt;/font&gt;&lt;/sub&gt; &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; para i de 1 a dim-1 faça &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; soma := 0 &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; para j de 0 a i-1 faça &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; soma = soma + f&lt;sub&gt;&lt;font size=2&gt;i,j&lt;/font&gt;&lt;/sub&gt;*VetY&lt;sub&gt;&lt;font size=2&gt;j&lt;/font&gt;&lt;/sub&gt; &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim para &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; VetY&lt;sub&gt;&lt;font size=2&gt;i&lt;/font&gt;&lt;/sub&gt; := (f&lt;sub&gt;&lt;font size=2&gt;i,dim&lt;/font&gt;&lt;/sub&gt;-soma)/f&lt;sub&gt;&lt;font size=2&gt;i,i&lt;/font&gt;&lt;/sub&gt; &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim para &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; retorna VetY &lt;br&gt;
        fim função &lt;br&gt; &lt;br&gt;
        se A = transposta(A,dim) então // a matriz é simétrica &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; para i de 0 a dim-1 faça &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; para j de 0 a  dim-1 faça //inicializar valores &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; U&lt;sub&gt;&lt;font size=2&gt;i,j&lt;/font&gt;&lt;/sub&gt; := 0  &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; Ut&lt;sub&gt;&lt;font size=2&gt;i,j&lt;/font&gt;&lt;/sub&gt; := 0 &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim para &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim para &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; para i de 0 a dim-1 faça &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; para j de 0 a dim-1 faça &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; se i = j então &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; somatmp := 0 &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; para k de 0 a j-1 faça &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; somatmp := somatmp + U&lt;sub&gt;&lt;font size=2&gt;k,i&lt;/font&gt;&lt;/sub&gt;*U&lt;sub&gt;&lt;font size=2&gt;k,i&lt;/font&gt;&lt;/sub&gt; &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim para &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; U&lt;sub&gt;&lt;font size=2&gt;i,i&lt;/font&gt;&lt;/sub&gt; := raizquadrada(A&lt;sub&gt;&lt;font size=2&gt;i,i&lt;/font&gt;&lt;/sub&gt;-somatmp) &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim se &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; se j &gt; i então &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; somatmp := 0 &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; para k de 0 a i-1 faça &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; somatmp := somatmp + U&lt;sub&gt;&lt;font size=2&gt;k,i&lt;/font&gt;&lt;/sub&gt;*U&lt;sub&gt;&lt;font size=2&gt;k,j&lt;/font&gt;&lt;/sub&gt; &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim para &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; U&lt;sub&gt;&lt;font size=2&gt;i,j&lt;/font&gt;&lt;/sub&gt; := (1/U&lt;sub&gt;&lt;font size=2&gt;i,i&lt;/font&gt;&lt;/sub&gt;)*(A&lt;sub&gt;&lt;font size=2&gt;i,j&lt;/font&gt;&lt;/sub&gt;-somatmp) &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim se &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim para &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim para &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; Ut := transposta(U) &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; para i de 0 a dim-1 faça &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; para j de 0 a dim faça &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; se j = dim então &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; Ut&lt;sub&gt;&lt;font size=2&gt;i,j&lt;/font&gt;&lt;/sub&gt; := T&lt;sub&gt;&lt;font size=2&gt;i&lt;/font&gt;&lt;/sub&gt; &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim se &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; senão &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; Ut&lt;sub&gt;&lt;font size=2&gt;i,j&lt;/font&gt;&lt;/sub&gt; := Ut&lt;sub&gt;&lt;font size=2&gt;i,j&lt;/font&gt;&lt;/sub&gt; &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim senão &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim para &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim para     &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; VetY := forwardsubstituição(Ut,dim) &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; para i de 0 a dim-1 faça &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; para j de 0 a dim faça &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; se j = dim então &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; U&lt;sub&gt;&lt;font size=2&gt;i,j&lt;/font&gt;&lt;/sub&gt; := VetY&lt;sub&gt;&lt;font size=2&gt;i&lt;/font&gt;&lt;/sub&gt; &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim se &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; senão &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; U&lt;sub&gt;&lt;font size=2&gt;i,j&lt;/font&gt;&lt;/sub&gt; := U&lt;sub&gt;&lt;font size=2&gt;i,j&lt;/font&gt;&lt;/sub&gt; &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim senão &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim para &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim para &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; VetX := retrosubstituição(U,dim) &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; retorna VetX &lt;br&gt;
        fim se &lt;br&gt;
        senão 'O método não pode ser executado pois a matriz não é simétrica.' </traducao>
    <traducao xml:lang="en-us"/>
  </sentenca>
  <sentenca xml:id="CHOLESKY_AJUDA">
    <traducao xml:lang="pt-br">
        &lt;ul&gt;
        &lt;li&gt;Os arquivos devem estar no formato .txt.&lt;/li&gt; &lt;br&gt;
        &lt;li&gt;Cada linha deve conter apenas &lt;b&gt;um&lt;/b&gt; valor, na seguinte ordem: &lt;/li&gt; &lt;br&gt;
        &lt;li&gt; &lt;b&gt; Arquivo de dados &lt;/b&gt;
        &lt;br&gt;
        &lt;br&gt; 1ª linha: dimensão da matriz A. &lt;br&gt;
        &lt;br&gt; A partir da 2ª linha: elementos da matriz A, a partir da primeira linha. Ao final de cada linha, inserir o valor do vetor B, tal que A x = B. &lt;br&gt;
        &lt;br&gt;
        &lt;li&gt; &lt;b&gt; Arquivo de resposta &lt;/b&gt;
        &lt;br&gt;
        &lt;br&gt; A partir da 1ª linha: elementos do vetor resposta. &lt;br&gt;
        &lt;/ul&gt;
    </traducao>
    <traducao xml:lang="en-us"/>
  </sentenca>
  <sentenca xml:id="DECMAT_MSG_01">
    <traducao xml:lang="pt-br">Decomposição de Matrizes - Verificação</traducao>
    <traducao xml:lang="en-us">Decomposition of Matrices - Verification</traducao>
  </sentenca>
  <sentenca xml:id="DECMAT_MSG_02">
    <traducao xml:lang="pt-br">Aritmética Matricial</traducao>
    <traducao xml:lang="en-us">Matricial Arithmetic</traducao>
  </sentenca>
  <sentenca xml:id="DECMAT_MSG_03">
    <traducao xml:lang="pt-br">Decomposição de Matrizes</traducao>
    <traducao xml:lang="en-us">Decomposition of matrices</traducao>
  </sentenca>
  <sentenca xml:id="DECMAT_MSG_04">
    <traducao xml:lang="pt-br">Dimensão: </traducao>
    <traducao xml:lang="en-us">Dimension:</traducao>
  </sentenca>
  <sentenca xml:id="DECMAT_MSG_05">
    <traducao xml:lang="pt-br">Matriz A</traducao>
    <traducao xml:lang="en-us">Matrix A</traducao>
  </sentenca>
  <sentenca xml:id="DECMAT_MSG_06">
    <traducao xml:lang="pt-br">Resposta obtida do arquivo:</traducao>
    <traducao xml:lang="en-us">Answer obtained from file:</traducao>
  </sentenca>
  <sentenca xml:id="DECMAT_MSG_07">
    <traducao xml:lang="pt-br">Resposta obtida do programa: </traducao>
    <traducao xml:lang="en-us">Answer obtained from the program: </traducao>
  </sentenca>
  <sentenca xml:id="DECMAT_MSG_08">
    <traducao xml:lang="pt-br">Determinantes das submatrizes: </traducao>
    <traducao xml:lang="en-us">Determinants of the submatrices: </traducao>
  </sentenca>
  <sentenca xml:id="DECMAT_MSG_09">
    <traducao xml:lang="pt-br">A matriz pode ser decomposta, pois nenhuma das determinantes é igual a 0.</traducao>
    <traducao xml:lang="en-us">The matrix can be decomposed, no determinant is equal to 0.</traducao>
  </sentenca>
  <sentenca xml:id="DECMAT_MSG_10">
    <traducao xml:lang="pt-br">A matriz não pode ser decomposta.</traducao>
    <traducao xml:lang="en-us">The matrix cannot be decomposed.</traducao>
  </sentenca>
  <sentenca xml:id="DECMAT_MSG_11">
    <traducao xml:lang="pt-br">Submatriz </traducao>
    <traducao xml:lang="en-us">Submatrix </traducao>
  </sentenca>
  <sentenca xml:id="DECMAT_MSG_12">
    <traducao xml:lang="pt-br">Determinante da submatriz </traducao>
    <traducao xml:lang="en-us">Determinant of the submatrix </traducao>
  </sentenca>
  <sentenca xml:id="DECMAT_ALGORITMO">
    <traducao xml:lang="pt-br">
        &lt;b&gt;Variáveis: &lt;/b&gt; &lt;br&gt;&lt;br&gt; 
        Auxiliares: &lt;br&gt;
        i, j (contadores), vetor, positiva (booleano) &lt;br&gt;&lt;br&gt;
        De entrada: &lt;br&gt;
        A (matriz), dim (dimensão da matriz) &lt;br&gt;&lt;br&gt;
        De saída: &lt;br&gt;
        booleano (positivo ou negativo) &lt;br&gt;&lt;br&gt;
        &lt;b&gt;Algoritmo: &lt;/b&gt; &lt;br&gt;&lt;br&gt; 
        decomp := sim &lt;br&gt;
        para i de 0 a dim-2 faça &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; vetor&lt;sub&gt;&lt;font size=2&gt;i&lt;/font&gt;&lt;/sub&gt; := determinante (A&lt;sub&gt;&lt;font size=2&gt;i,i&lt;/font&gt;&lt;/sub&gt;) , onde A&lt;sub&gt;&lt;font size=2&gt;i,i&lt;/font&gt;&lt;/sub&gt; é a submatriz de A, de dimensão i &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; se vetor&lt;sub&gt;&lt;font size=2&gt;i&lt;/font&gt;&lt;/sub&gt; = 0 então &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; decomp := nao &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim se &lt;br&gt;  
        fim para i &lt;br&gt;
        se decomp = nao então &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; retorna 'A matriz não pode ser decomposta.' &lt;br&gt;
        fim se &lt;br&gt;
        senão &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; retorna 'A matriz pode ser decomposta.' &lt;br&gt;
        fim senão </traducao>
    <traducao xml:lang="en-us"/>
  </sentenca>
  <sentenca xml:id="DECMAT_AJUDA">
    <traducao xml:lang="pt-br">
        &lt;ul&gt;
        &lt;li&gt;Os arquivos devem estar no formato .txt.&lt;/li&gt; &lt;br&gt;
        &lt;li&gt;Cada linha deve conter apenas &lt;b&gt;um&lt;/b&gt; valor, na seguinte ordem: &lt;/li&gt; &lt;br&gt;
        &lt;li&gt; &lt;b&gt; Arquivo de dados &lt;/b&gt;
        &lt;br&gt;
        &lt;br&gt; 1ª linha: dimensão da matriz A. &lt;br&gt;
        &lt;br&gt; A partir da 2ª linha: elementos da matriz A, em ordem crescente de coluna e linha. &lt;br&gt;
        &lt;br&gt;
        &lt;li&gt; &lt;b&gt; Arquivo de resposta &lt;/b&gt;
        &lt;br&gt;
        &lt;br&gt; 1ª linha: determinante da submatriz 1 x 1. &lt;br&gt;
        &lt;br&gt; 2ª linha: determinante da submatriz 2 x 2. &lt;br&gt;   
        &lt;br&gt; nª linha: determinante da submatriz n x n. &lt;br&gt; 
        &lt;br&gt; Última linha: 
        &lt;br&gt; 1 - caso a matriz seja definida positiva
        &lt;br&gt; 0 - caso a matriz não seja definida positiva
        &lt;/ul&gt;      </traducao>
    <traducao xml:lang="en-us"/>
  </sentenca>
  <sentenca xml:id="DERIVADA_MSG_01">
    <traducao xml:lang="pt-br">Derivadas</traducao>
    <traducao xml:lang="en-us">Derivatives</traducao>
  </sentenca>
  <sentenca xml:id="DERIVADA_MSG_02">
    <traducao xml:lang="pt-br">Derivação numérica</traducao>
    <traducao xml:lang="en-us">Numerical derivative</traducao>
  </sentenca>
  <sentenca xml:id="DERIVADA_MSG_03a">
    <traducao xml:lang="pt-br">Método da diferença central</traducao>
    <traducao xml:lang="en-us">Central diference method</traducao>
  </sentenca>
  <sentenca xml:id="DERIVADA_MSG_04">
    <traducao xml:lang="pt-br">Digite a função: </traducao>
    <traducao xml:lang="en-us">Type the function: </traducao>
  </sentenca>
  <sentenca xml:id="DERIVADA_MSG_06">
    <traducao xml:lang="pt-br">Digite o número máximo de iterações k: </traducao>
    <traducao xml:lang="en-us">Type the maximum number of iterations k: </traducao>
  </sentenca>
  <sentenca xml:id="DERIVADA_MSG_07">
    <traducao xml:lang="pt-br">Calcular derivada da f(x) para x = </traducao>
    <traducao xml:lang="en-us">Calculate derivative of f(x), where x = </traducao>
  </sentenca>
  <sentenca xml:id="DERIVADA_MSG_08">
    <traducao xml:lang="pt-br">Função: </traducao>
    <traducao xml:lang="en-us">Function: </traducao>
  </sentenca>
  <sentenca xml:id="DERIVADA_MSG_09">
    <traducao xml:lang="pt-br">Precisão t da resposta: </traducao>
    <traducao xml:lang="en-us">Precision t of the answer: </traducao>
  </sentenca>
  <sentenca xml:id="DERIVADA_MSG_10">
    <traducao xml:lang="pt-br">Resposta retirada do arquivo: </traducao>
    <traducao xml:lang="en-us">Answer obtained from file: </traducao>
  </sentenca>
  <sentenca xml:id="DERIVADA_MSG_11">
    <traducao xml:lang="pt-br">Derivada no ponto x=</traducao>
    <traducao xml:lang="en-us">Derivative on the point x=</traducao>
  </sentenca>
  <sentenca xml:id="DERIVADA_MSG_12">
    <traducao xml:lang="pt-br">Número máximo de iterações k: </traducao>
    <traducao xml:lang="en-us">Maximum number of iterations k: </traducao>
  </sentenca>
  <sentenca xml:id="DERIVADA_MSG_13">
    <traducao xml:lang="pt-br">Erro relativo da resposta: </traducao>
    <traducao xml:lang="en-us">Relative error of the answer: </traducao>
  </sentenca>
  <sentenca xml:id="DERIVADA_MSG_14">
    <traducao xml:lang="pt-br">Resposta obtida do programa: </traducao>
    <traducao xml:lang="en-us">Answer obtained from the program: </traducao>
  </sentenca>
  <sentenca xml:id="DERIVADA_MSG_15">
    <traducao xml:lang="pt-br">Resposta obtida do arquivo: </traducao>
    <traducao xml:lang="en-us">Answer obtained from file: </traducao>
  </sentenca>
  <sentenca xml:id="DERIVADA_MSG_16">
    <traducao xml:lang="pt-br">O método não convergiu para a resposta. Tente utilizar outros parâmetros para número de iterações, precisão e margem de erro da resposta. </traducao>
    <traducao xml:lang="en-us">The method did not converge for the answer. Try to user other parameters for the number of iterations, precision e error margin of the answer. </traducao>
  </sentenca>
  <sentenca xml:id="DERIVADA_MSG_17">
    <traducao xml:lang="pt-br">'Calcular a derivada em outro ponto' </traducao>
    <traducao xml:lang="en-us">'Calculate the derivative on other point'</traducao>
  </sentenca>
  <sentenca xml:id="DERIVADA_ALGORITMO">
    <traducao xml:lang="pt-br">
        &lt;b&gt;Variáveis: &lt;/b&gt; &lt;br&gt;&lt;br&gt; 
        Auxiliares: &lt;br&gt;
        j (contador), f0, f1, x, t (no programa possui valor fixo igual a 10), hk, derivada0, derivada1, para &lt;br&gt;&lt;br&gt;
        De entrada: &lt;br&gt;
        função (na sintaxe reconhecida pelo programa), k (número de iterações), erro (erro relativo da resposta), xo (valor de x para o cálculo da derivada)  &lt;br&gt;&lt;br&gt;
        De saída: &lt;br&gt;
        resposta&lt;br&gt;&lt;br&gt;
        &lt;b&gt;Algoritmo: &lt;/b&gt; &lt;br&gt;&lt;br&gt; 
        função deriva(funcao,k,t,xo,erro) &lt;br&gt; 
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; para := falso &lt;br&gt; 
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; j := 1 &lt;br&gt; 
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; hk := t&lt;sup&gt;-j&lt;/sup&gt; &lt;br&gt; 
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; x := xo-hk &lt;br&gt; 
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; f0 := valor da funcao no ponto x &lt;br&gt; 
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; x := xo+hk &lt;br&gt; 
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; f1 := valor da funcao no ponto x &lt;br&gt; 
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; derivada0 := (f1-f0)/(2*hk) &lt;br&gt; 
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; enquanto (para = falso) e (j &lt;= k) faça &lt;br&gt; 
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; j := j + 1 &lt;br&gt; 
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; hk := t&lt;sup&gt;-j&lt;/sup&gt; &lt;br&gt; 
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; x := xo-hk &lt;br&gt; 
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; f0 := valor da funcao no ponto x &lt;br&gt; 
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; x := xo+hk &lt;br&gt; 
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; derivada1 := (f1-f0)/(2*hk) &lt;br&gt; 
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; se (derivada1-derivada0) &lt; erro então &lt;br&gt; 
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; para := verdadeiro &lt;br&gt; 
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim se &lt;br&gt; 
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; derivada0 := derivada1 &lt;br&gt; 
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim enquanto &lt;br&gt; 
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; se (para = verdadeiro) e (derivada0 é um número válido) então &lt;br&gt; 
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; resposta := derivada0 &lt;br&gt; 
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim se &lt;br&gt; 
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; senão se (j&gt;k) ou (derivada0 não é um número válido) então &lt;br&gt; 
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; resposta = 'erro' &lt;br&gt; 
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; retorna resposta &lt;br&gt; 
        fim função </traducao>
    <traducao xml:lang="en-us"/>
  </sentenca>
  <sentenca xml:id="DERIVADA_AJUDA">
    <traducao xml:lang="pt-br">
        &lt;ul&gt;
        &lt;li&gt;Os arquivos devem estar no formato .txt.&lt;/li&gt; &lt;br&gt;
        &lt;li&gt;Cada linha deve conter apenas &lt;b&gt;um&lt;/b&gt;, na seguinte ordem: &lt;/li&gt; &lt;br&gt;
        &lt;li&gt; &lt;b&gt; Arquivo de dados &lt;/b&gt;
        &lt;br&gt;
        &lt;br&gt; 1ª linha: função do problema, no &lt;a href=javascript:winopen('funcoesphp.php')&gt;formato&lt;/a&gt; reconhecido pelo programa. &lt;br&gt;
        &lt;br&gt; 2ª linha: número de iterações k. &lt;br&gt;
        &lt;br&gt; 3ª linha: erro relativo da resposta. &lt;br&gt;
        &lt;br&gt; 4ª linha: valor de x para cálculo da derivada. &lt;br&gt;
        &lt;br&gt;
        &lt;li&gt; &lt;b&gt; Arquivo de resposta &lt;/b&gt;
        &lt;br&gt;
        &lt;br&gt; 1ª linha: resultado da derivada ou 'erro' caso não haja resposta. &lt;br&gt;
        &lt;/ul&gt;
    </traducao>
    <traducao xml:lang="en-us"/>
  </sentenca>
  <sentenca xml:id="DETERMINANTE_MSG_01">
    <traducao xml:lang="pt-br">Determinante de Matrizes - triangularização</traducao>
    <traducao xml:lang="en-us">Determinant of Matrices - triangularization</traducao>
  </sentenca>
  <sentenca xml:id="DETERMINANTE_MSG_02">
    <traducao xml:lang="pt-br">Aritmética Matricial</traducao>
    <traducao xml:lang="en-us">Matricial Arithmetic</traducao>
  </sentenca>
  <sentenca xml:id="DETERMINANTE_MSG_03">
    <traducao xml:lang="pt-br">Determinante</traducao>
    <traducao xml:lang="en-us">Determinant</traducao>
  </sentenca>
  <sentenca xml:id="DETERMINANTE_MSG_04">
    <traducao xml:lang="pt-br">Dimensão: </traducao>
    <traducao xml:lang="en-us">Dimension: </traducao>
  </sentenca>
  <sentenca xml:id="DETERMINANTE_MSG_05">
    <traducao xml:lang="pt-br">Matriz A</traducao>
    <traducao xml:lang="en-us">Matrix A</traducao>
  </sentenca>
  <sentenca xml:id="DETERMINANTE_MSG_06">
    <traducao xml:lang="pt-br">Resposta obtida do arquivo: </traducao>
    <traducao xml:lang="en-us">Answer obtained from file: </traducao>
  </sentenca>
  <sentenca xml:id="DETERMINANTE_MSG_07">
    <traducao xml:lang="pt-br">Valor do derminante = </traducao>
    <traducao xml:lang="en-us">Determinant value = </traducao>
  </sentenca>
  <sentenca xml:id="DETERMINANTE_MSG_08">
    <traducao xml:lang="pt-br">A matriz não possui determinante.</traducao>
    <traducao xml:lang="en-us">The matrix does not have a determinant.</traducao>
  </sentenca>
  <sentenca xml:id="DETERMINANTE_MSG_09">
    <traducao xml:lang="pt-br"> passo:</traducao>
    <traducao xml:lang="en-us"> step:</traducao>
  </sentenca>
  <sentenca xml:id="DETERMINANTE_MSG_10">
    <traducao xml:lang="pt-br">Resposta obtida do programa: </traducao>
    <traducao xml:lang="en-us">Answer obtained from the program: </traducao>
  </sentenca>
  <sentenca xml:id="DETERMINANTE_EXE_01">
    <traducao xml:lang="pt-br">Matriz de dimensão 2</traducao>
    <traducao xml:lang="en-us">Matrix of dimension 2</traducao>
  </sentenca>
  <sentenca xml:id="DETERMINANTE_EXE_02">
    <traducao xml:lang="pt-br">Matriz de dimensão 3</traducao>
    <traducao xml:lang="en-us">Matrix of dimension 3</traducao>
  </sentenca>
  <sentenca xml:id="DETERMINANTE_EXE_03">
    <traducao xml:lang="pt-br">Matriz de dimensão 4</traducao>
    <traducao xml:lang="en-us">Matrix of dimension 4</traducao>
  </sentenca>
  <sentenca xml:id="DETERMINANTE_ALGORITMO">
    <traducao xml:lang="pt-br">&lt;b&gt;Variáveis: &lt;/b&gt; &lt;br&gt;&lt;br&gt; 
        Auxiliares: &lt;br&gt;
        i, j, k, l, cont (contadores), M (matriz), aux, troca, indice, maior &lt;br&gt;&lt;br&gt;
        De entrada: &lt;br&gt;
        A (matriz), dim (dimensão da matriz) &lt;br&gt;&lt;br&gt;
        De saída: &lt;br&gt;
        det &lt;br&gt;&lt;br&gt;
        &lt;b&gt;Algoritmo: &lt;/b&gt; &lt;br&gt;&lt;br&gt; 
        det := 1 &lt;br&gt;
        para k de 0 a dim-1 faça &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; para i de k+1 até dim-1 faça &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; se A&lt;sub&gt;&lt;font size=2&gt;k,k&lt;/font&gt;&lt;/sub&gt; = 0 então   // pivô se anula    &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; maior := módulo(A&lt;sub&gt;&lt;font size=2&gt;k,k&lt;/font&gt;&lt;/sub&gt;) &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; para cont de k+1 a dim-1 faça &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; se módulo(A&lt;sub&gt;&lt;font size=2&gt;cont,k&lt;/font&gt;&lt;/sub&gt;) &gt; maior então &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; maior := módulo(A&lt;sub&gt;&lt;font size=2&gt;cont,k&lt;/font&gt;&lt;/sub&gt;) &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; indice := cont &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim se &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim para cont &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; troca := indice + 1 &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; para l de 0 a dim-1 faça   //troca de linha &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; aux2 := A&lt;sub&gt;&lt;font size=2&gt;k,l&lt;/font&gt;&lt;/sub&gt; &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; A&lt;sub&gt;&lt;font size=2&gt;k,l&lt;/font&gt;&lt;/sub&gt; := A&lt;sub&gt;&lt;font size=2&gt;indice,l&lt;/font&gt;&lt;/sub&gt; &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; A&lt;sub&gt;&lt;font size=2&gt;indice,l&lt;/font&gt;&lt;/sub&gt; := aux2 &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim para l &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; det := -det &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim se &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; M&lt;sub&gt;&lt;font size=2&gt;i,k&lt;/font&gt;&lt;/sub&gt; := M&lt;sub&gt;&lt;font size=2&gt;i,k&lt;/font&gt;&lt;/sub&gt; - A&lt;sub&gt;&lt;font size=2&gt;i,k&lt;/font&gt;&lt;/sub&gt; / A&lt;sub&gt;&lt;font size=2&gt;k,k&lt;/font&gt;&lt;/sub&gt; &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; para j de 0 a dim-1 faça &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; A&lt;sub&gt;&lt;font size=2&gt;i,j&lt;/font&gt;&lt;/sub&gt; := A&lt;sub&gt;&lt;font size=2&gt;i,j&lt;/font&gt;&lt;/sub&gt; + M&lt;sub&gt;&lt;font size=2&gt;i,k&lt;/font&gt;&lt;/sub&gt;*A&lt;sub&gt;&lt;font size=2&gt;k,j&lt;/font&gt;&lt;/sub&gt; &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim para j &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim para i &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; det := det * A&lt;sub&gt;&lt;font size=2&gt;i,i&lt;/font&gt;&lt;/sub&gt; &lt;br&gt;
        fim para k &lt;br&gt;
        retorna det &lt;br&gt;
    </traducao>
    <traducao xml:lang="en-us"/>
  </sentenca>
  <sentenca xml:id="DETERMINANTE_AJUDA">
    <traducao xml:lang="pt-br">
        &lt;ul&gt;
        &lt;li&gt;Os arquivos devem estar no formato .txt.&lt;/li&gt; &lt;br&gt;
        &lt;li&gt;Cada linha deve conter apenas &lt;b&gt;um&lt;/b&gt; valor, na seguinte ordem: &lt;/li&gt; &lt;br&gt; 
        &lt;li&gt; &lt;b&gt; Arquivo de dados &lt;/b&gt;
        &lt;br&gt;
        &lt;br&gt; 1ª linha: dimensão da matriz A. &lt;br&gt;
        &lt;br&gt; A partir da 2ª linha: elementos da matriz A, em ordem crescente de coluna e linha. &lt;br&gt;
        &lt;br&gt;
        &lt;li&gt; &lt;b&gt; Arquivo de resposta &lt;/b&gt;
        &lt;br&gt;
        &lt;br&gt; A partir da 1ª linha: elementos da matriz B, em ordem crescente de coluna e linha. &lt;br&gt;
        &lt;/ul&gt;
    </traducao>
    <traducao xml:lang="en-us"/>
  </sentenca>
  <sentenca xml:id="EQNL_MSG_01">
    <traducao xml:lang="pt-br">Equações não-lineares</traducao>
    <traducao xml:lang="en-us">Nonlinear equations</traducao>
  </sentenca>
  <sentenca xml:id="EQNL_MSG_02">
    <traducao xml:lang="pt-br">Resolução de equações não-lineares</traducao>
    <traducao xml:lang="en-us">Nonlinear equations solving</traducao>
  </sentenca>
  <sentenca xml:id="EQNL_MSG_03a">
    <traducao xml:lang="pt-br">Método da Secante</traducao>
    <traducao xml:lang="en-us">Secant method</traducao>
  </sentenca>
  <sentenca xml:id="EQNL_MSG_03b">
    <traducao xml:lang="pt-br">Método da Bissecção</traducao>
    <traducao xml:lang="en-us">Bisection method</traducao>
  </sentenca>
  <sentenca xml:id="EQNL_MSG_03c">
    <traducao xml:lang="pt-br">Método de Newton</traducao>
    <traducao xml:lang="en-us">Newton's Method</traducao>
  </sentenca>
  <sentenca xml:id="EQNL_MSG_03d">
    <traducao xml:lang="pt-br">Gráfico</traducao>
    <traducao xml:lang="en-us">Graphic</traducao>
  </sentenca>
  <sentenca xml:id="EQNL_MSG_04">
    <traducao xml:lang="pt-br">Digite o grau do polinômio: </traducao>
    <traducao xml:lang="en-us">Type the degree of the polynom: </traducao>
  </sentenca>
  <sentenca xml:id="EQNL_MSG_05">
    <traducao xml:lang="pt-br">Digite os coeficientes da equação: </traducao>
    <traducao xml:lang="en-us">Type the coefficients of the equation: </traducao>
  </sentenca>
  <sentenca xml:id="EQNL_MSG_06">
    <traducao xml:lang="pt-br">Digite o erro relativo: </traducao>
    <traducao xml:lang="en-us">Type the relative error: </traducao>
  </sentenca>
  <sentenca xml:id="EQNL_MSG_07">
    <traducao xml:lang="pt-br">Digite o número máximo de iterações: </traducao>
    <traducao xml:lang="en-us">Type the maximum number of iterations: </traducao>
  </sentenca>
  <sentenca xml:id="EQNL_MSG_08">
    <traducao xml:lang="pt-br">Equação dada: </traducao>
    <traducao xml:lang="en-us">Given equation: </traducao>
  </sentenca>
  <sentenca xml:id="EQNL_MSG_09">
    <traducao xml:lang="pt-br">Grau do polinômio: </traducao>
    <traducao xml:lang="en-us">Degree of the polynom: </traducao>
  </sentenca>
  <sentenca xml:id="EQNL_MSG_10">
    <traducao xml:lang="pt-br">Erro relativo: </traducao>
    <traducao xml:lang="en-us">Relative error:</traducao>
  </sentenca>
  <sentenca xml:id="EQNL_MSG_11">
    <traducao xml:lang="pt-br">Número máximo de iterações: </traducao>
    <traducao xml:lang="en-us">Maximum number of iterations: </traducao>
  </sentenca>
  <sentenca xml:id="EQNL_MSG_12">
    <traducao xml:lang="pt-br">Enumeração de raízes - Quadro de possibilidades</traducao>
    <traducao xml:lang="en-us">Enumeration of roots - Possibilities table</traducao>
  </sentenca>
  <sentenca xml:id="EQNL_MSG_13">
    <traducao xml:lang="pt-br">Raízes reais positivas</traducao>
    <traducao xml:lang="en-us">Real positive roots</traducao>
  </sentenca>
  <sentenca xml:id="EQNL_MSG_14">
    <traducao xml:lang="pt-br">Raízes reais negativas</traducao>
    <traducao xml:lang="en-us">Real negative roots</traducao>
  </sentenca>
  <sentenca xml:id="EQNL_MSG_15">
    <traducao xml:lang="pt-br">Raízes complexas</traducao>
    <traducao xml:lang="en-us">Complex roots</traducao>
  </sentenca>
  <sentenca xml:id="EQNL_MSG_16">
    <traducao xml:lang="pt-br">Total</traducao>
    <traducao xml:lang="en-us">Total</traducao>
  </sentenca>
  <sentenca xml:id="EQNL_MSG_17">
    <traducao xml:lang="pt-br">Localização de raízes</traducao>
    <traducao xml:lang="en-us">Localization of roots - Quota of Laguerre-Thibault</traducao>
  </sentenca>
  <sentenca xml:id="EQNL_MSG_18">
    <traducao xml:lang="pt-br">Cota inferior</traducao>
    <traducao xml:lang="en-us">Lower quota</traducao>
  </sentenca>
  <sentenca xml:id="EQNL_MSG_19">
    <traducao xml:lang="pt-br">Cota superior</traducao>
    <traducao xml:lang="en-us">Upper quota</traducao>
  </sentenca>
  <sentenca xml:id="EQNL_MSG_20a">
    <traducao xml:lang="pt-br">Digite o valor de x&lt;sub&gt;0&lt;/sub&gt; e de x&lt;sub&gt;1&lt;/sub&gt; (estimativa inicial):</traducao>
    <traducao xml:lang="en-us">Type the value of x&lt;sub&gt;0&lt;/sub&gt; and de x&lt;sub&gt;1&lt;/sub&gt; (initial estimate):</traducao>
  </sentenca>
  <sentenca xml:id="EQNL_MSG_20b">
    <traducao xml:lang="pt-br">Digite o intervalo desejado:</traducao>
    <traducao xml:lang="en-us">Type the interval: </traducao>
  </sentenca>
  <sentenca xml:id="EQNL_MSG_20c">
    <traducao xml:lang="pt-br">Digite a estimativa inicial x&lt;sub&gt;0&lt;/sub&gt;:</traducao>
    <traducao xml:lang="en-us">Type an initial estimate x&lt;sub&gt;0&lt;/sub&gt;:</traducao>
  </sentenca>
  <sentenca xml:id="EQNL_MSG_21">
    <traducao xml:lang="pt-br">Resposta retirada do arquivo: </traducao>
    <traducao xml:lang="en-us">Extracted answer of the archive:</traducao>
  </sentenca>
  <sentenca xml:id="EQNL_MSG_22">
    <traducao xml:lang="pt-br">O método convergiu para </traducao>
    <traducao xml:lang="en-us">The method converged to </traducao>
  </sentenca>
  <sentenca xml:id="EQNL_MSG_23">
    <traducao xml:lang="pt-br"> em </traducao>
    <traducao xml:lang="en-us"> in </traducao>
  </sentenca>
  <sentenca xml:id="EQNL_MSG_24">
    <traducao xml:lang="pt-br"> iterações.</traducao>
    <traducao xml:lang="en-us"> iterations.</traducao>
  </sentenca>
  <sentenca xml:id="EQNL_MSG_25">
    <traducao xml:lang="pt-br">'Plotar gráfico'</traducao>
    <traducao xml:lang="en-us">'Plot the graphic'</traducao>
  </sentenca>
  <sentenca xml:id="EQNL_MSG_26a">
    <traducao xml:lang="pt-br">Valores de x&lt;sub&gt;0&lt;/sub&gt; e x&lt;sub&gt;1&lt;/sub&gt;:</traducao>
    <traducao xml:lang="en-us">Values of x&lt;sub&gt;0&lt;/sub&gt; e x&lt;sub&gt;1&lt;/sub&gt;:</traducao>
  </sentenca>
  <sentenca xml:id="EQNL_MSG_26b">
    <traducao xml:lang="pt-br">Intervalo definido: </traducao>
    <traducao xml:lang="en-us">Defined interval: </traducao>
  </sentenca>
  <sentenca xml:id="EQNL_MSG_26c">
    <traducao xml:lang="pt-br">Estimativa inicial x&lt;sub&gt;0&lt;/sub&gt;: </traducao>
    <traducao xml:lang="en-us">Initial estimative x&lt;sub&gt;0&lt;/sub&gt;: </traducao>
  </sentenca>
  <sentenca xml:id="EQNL_MSG_27">
    <traducao xml:lang="pt-br">Iteração</traducao>
    <traducao xml:lang="en-us">Iterations</traducao>
  </sentenca>
  <sentenca xml:id="EQNL_MSG_28">
    <traducao xml:lang="pt-br">Resposta obtida do programa: </traducao>
    <traducao xml:lang="en-us">Gotten answer of the program: </traducao>
  </sentenca>
  <sentenca xml:id="EQNL_MSG_29">
    <traducao xml:lang="pt-br">O zero encontrado é exato: </traducao>
    <traducao xml:lang="en-us">The found root is exact: </traducao>
  </sentenca>
  <sentenca xml:id="EQNL_MSG_30">
    <traducao xml:lang="pt-br">Esses valores fazem parte do conjunto de raízes da equação</traducao>
    <traducao xml:lang="en-us">These values are part of the set of roots of the equation</traducao>
  </sentenca>
  <sentenca xml:id="EQNL_MSG_31">
    <traducao xml:lang="pt-br">O denominador anula-se durante o processo utilizando estes valores iniciais</traducao>
    <traducao xml:lang="en-us">The denominator was annulled during the process using these initial values</traducao>
  </sentenca>
  <sentenca xml:id="EQNL_MSG_32">
    <traducao xml:lang="pt-br">O método não convergiu após </traducao>
    <traducao xml:lang="en-us">The method did not converg after </traducao>
  </sentenca>
  <sentenca xml:id="EQNL_MSG_33">
    <traducao xml:lang="pt-br"> iterações</traducao>
    <traducao xml:lang="en-us"> iterations.</traducao>
  </sentenca>
  <sentenca xml:id="EQNL_MSG_34">
    <traducao xml:lang="pt-br">Resposta obtida do arquivo:</traducao>
    <traducao xml:lang="en-us">Gotten answer of the archive:</traducao>
  </sentenca>
  <sentenca xml:id="EQNL_MSG_35">
    <traducao xml:lang="pt-br">'Digitar outras estimativas'</traducao>
    <traducao xml:lang="en-us">'Type other estimates'</traducao>
  </sentenca>
  <sentenca xml:id="EQNL_MSG_36">
    <traducao xml:lang="pt-br">Não existem raízes neste intervalo. Digite outro intervalo</traducao>
    <traducao xml:lang="en-us">There are no roots in this interval. Type other interval.</traducao>
  </sentenca>
  <sentenca xml:id="EQNL_MSG_37">
      <traducao xml:lang="pt-br">Intervalo em 'x' onde será plotado o gráfico:</traducao>
      <traducao xml:lang="en-us">Interval in 'x' where the graphic will be ploted:</traducao>
  </sentenca>
  <sentenca xml:id="EQNL_MSG_38">
      <traducao xml:lang="pt-br">'Limpar intervalo'</traducao>
      <traducao xml:lang="en-us">'Choose another interval'</traducao>
  </sentenca>
  <sentenca xml:id="EQNL_MSG_39">
      <traducao xml:lang="pt-br">'Retornar ao programa'</traducao>
      <traducao xml:lang="en-us">'Return to the program'</traducao>
  </sentenca>
  <sentenca xml:id="EQNL_MSG_40">
    <traducao xml:lang="pt-br">Digite a função de entrada:</traducao>
    <traducao xml:lang="en-us">Type the function of entrance:</traducao>
  </sentenca>
  <sentenca xml:id="EQNL_MSG_41">
    <traducao xml:lang="pt-br">Escolha o tipo de função de entrada:</traducao>
    <traducao xml:lang="en-us">Choose the type of function of entrance:</traducao>
  </sentenca>
  <sentenca xml:id="EQNL_MSG_42">
    <traducao xml:lang="pt-br">Através de um polinômio</traducao>
    <traducao xml:lang="en-us">A polynomial</traducao>
  </sentenca>
  <sentenca xml:id="EQNL_MSG_43">
    <traducao xml:lang="pt-br">Através de uma função qualquer</traducao>
    <traducao xml:lang="en-us">Another type of function</traducao>
  </sentenca>
  <sentenca xml:id="EQNL_MSG_44">
    <traducao xml:lang="pt-br">Não foi possível calcular o método. Tente outra estimativa.</traducao>
    <traducao xml:lang="en-us">It was not possible to calculate the method.  Try another estimate.</traducao>
  </sentenca>
  <sentenca xml:id="EQNL_EXEa_01">
    <traducao xml:lang="pt-br">Polinômio de grau 3, com erro relativo de 0.01</traducao>
    <traducao xml:lang="en-us">Polynomial of degree 3, with an relative error of 0.01</traducao>
  </sentenca>
  <sentenca xml:id="EQNL_ALGORITMOa">
    <traducao xml:lang="pt-br">
        &lt;b&gt;Variáveis: &lt;/b&gt; &lt;br&gt;&lt;br&gt; 
        Auxiliares: &lt;br&gt;
        i, j (contadores), resx0, resx1, resx2, aux, localerror, para, den &lt;br&gt;&lt;br&gt;
        De entrada: &lt;br&gt;
        deg (grau do polinômio) e coef (vetor de coeficientes do polinômio) ou uma função de entrada qualquer, x0 e x1 (estimativas iniciais), it (número de iterações), error (margem de erro da resposta)  &lt;br&gt;&lt;br&gt;
        De saída: &lt;br&gt;
        x2 (quando o método convergir para uma solução)&lt;br&gt;&lt;br&gt;
        &lt;b&gt;Algoritmo: &lt;/b&gt; &lt;br&gt;&lt;br&gt; 
        j:=0 &lt;br&gt;
        para:=não &lt;br&gt;
        enquanto (j&lt;=it) e (para diferente de sim) faça &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; j := j + 1 &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; resx1 := valor da função no ponto  x1 &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; resx0 := valor da função no ponto x0 &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; den := resx1-resx0 &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; se módulo(den) &gt;= error então &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; x2 := x1 - (resx1*(x1-x0)) / den &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; aux := máximo(1,módulo(x2)) &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; localerror := módulo(x2-x1) / aux &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; resx2 := 0 &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; para i de 0 a deg-1 faça &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; resx2 := resx2 + coef&lt;sub&gt;&lt;font size=2&gt;i&lt;/font&gt;&lt;/sub&gt; * x1&lt;sup&gt;deg-i&lt;/sup&gt; &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim para &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; resx2 := resx2 + coef&lt;sub&gt;&lt;font size=2&gt;deg&lt;/font&gt;&lt;/sub&gt; &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; se localerror &lt; error então &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; 'O método convergiu' &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; retorna x2 &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; para := sim &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim se &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; se resx2 = 0 então &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; 'O zero é exato' &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; retorna x2 &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; para := sim &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim se &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; se para é diferente de sim então &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; x0 := x1 &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; x1 := x2 &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim se &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim se &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; senão &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; se (resx0=0) e (resx1=0) então &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; 'Estes valores não fazem parte do conjunto de raízes da equação' &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim se &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; senão &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; 'O denominador anula-se durante o processo utilizando estes valores iniciais' &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim senão &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; O método não convergiu. &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; para := sim &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim senão &lt;br&gt;
        fim enquanto &lt;br&gt;
        se j &gt;= it então &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; 'O método não convergiu para este número de iterações' &lt;br&gt;
        fim se </traducao>
    <traducao xml:lang="en-us"/>
  </sentenca>
  <sentenca xml:id="EQNL_AJUDAa">
    <traducao xml:lang="pt-br">
        &lt;ul&gt;
        &lt;li&gt;Os arquivos devem estar no formato .txt.&lt;/li&gt; &lt;br&gt;
        &lt;li&gt;Cada linha deve conter apenas &lt;b&gt;um&lt;/b&gt; valor, na seguinte ordem: &lt;/li&gt; &lt;br&gt; 
        &lt;li&gt; &lt;b&gt; Arquivo de dados &lt;/b&gt;
        &lt;br&gt;
        &lt;br&gt; 1ª linha: '0' (zero) para calcular o método em um polinômio ou '1' para calcular o método em uma função qualquer. &lt;br&gt;
        &lt;br&gt; 2ª linha: caso a entrada seja através de um polinômio, digite o grau dele, senão, a função do problema, no &lt;a href=javascript:winopen('funcoesphp.php')&gt;formato&lt;/a&gt; reconhecido pelo programa. &lt;br&gt;
        &lt;br&gt; A partir da 3ª linha: coeficientes do polinômio para o caso polinomial, a partir do coeficiente que acompanha a variável de maior grau. Caso contrário, ignorar esta etapa.&lt;br&gt;
        &lt;br&gt; Em seguida: erro relativo para o resultado. &lt;br&gt;
        &lt;br&gt; Em seguida: número de iterações. &lt;br&gt;
        &lt;br&gt; Nas duas últimas linhas: valor de x0 e x1 (estimativas iniciais). &lt;br&gt;
        &lt;br&gt;
        &lt;li&gt; &lt;b&gt; Arquivo de resposta &lt;/b&gt;
        &lt;br&gt;
        &lt;br&gt; 1ª linha: 0 caso o método não tenha convergido, ou 1 caso contrário. &lt;br&gt;
        &lt;br&gt; 2ª linha: Valor da resposta, caso haja. &lt;br&gt;
        &lt;br&gt; 3ª linha: Número de iterações, caso haja resposta. &lt;br&gt;
        &lt;/ul&gt;
    </traducao>
    <traducao xml:lang="en-us"/>
  </sentenca>
  <sentenca xml:id="EQNL_EXEb_01">
    <traducao xml:lang="pt-br">Polinômio de grau 2, com erro relativo de 0.01</traducao>
    <traducao xml:lang="en-us"/>
  </sentenca>
  <sentenca xml:id="EQNL_EXEb_02">
    <traducao xml:lang="pt-br">Polinômio de grau 3, com erro relativo de 0.1</traducao>
    <traducao xml:lang="en-us"/>
  </sentenca>
  <sentenca xml:id="EQNL_ALGORITMOb">
    <traducao xml:lang="pt-br">
        &lt;b&gt;Variáveis: &lt;/b&gt; &lt;br&gt;&lt;br&gt; 
        Auxiliares: &lt;br&gt;
        i, j (contadores), fmin, fmax, min, max, aux, fmedio, para, volta, ok, den &lt;br&gt;&lt;br&gt;
        De entrada: &lt;br&gt;
        deg (grau do polinômio) e coef (vetor de coeficientes do polinômio) ou uma função de entrada qualquer, int1 e int2 (intervalo da função), it (número de iterações), error (margem de erro da resposta)  &lt;br&gt;&lt;br&gt;
        De saída: &lt;br&gt;
        xmedio (quando o método convergir para uma solução)&lt;br&gt;&lt;br&gt;
        &lt;b&gt;Algoritmo: &lt;/b&gt; &lt;br&gt;&lt;br&gt; 
        j := 1 &lt;br&gt;
        para := não &lt;br&gt;
        volta := não &lt;br&gt;
        ok := não &lt;br&gt;
        fmin := valor da função no ponto int1 &lt;br&gt;
        fmax := valor da função no ponto int2 &lt;br&gt;
        if (fmin*fmax)&gt;0 então &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; 'Neste intervalo não há solução' &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; volta := sim &lt;br&gt;
        fim se &lt;br&gt;
        senão &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; ok := sim &lt;br&gt;
        fim senão &lt;br&gt;
        se ok = sim então &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; min := int1 &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; max := int2 &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; enquanto (j &lt; it) e (para diferente de sim) faça &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; xmedio := (min+max) / 2 &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fmedio := valor da função no ponto xmedio &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; se ( (xmedio-min) &lt; error ) e (max-xmedio) &lt; error) então &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; 'O método convergiu' &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; retorna xmedio &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; para := sim &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim se &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; se fmedio=0 então &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; 'O zero encontrado é exato' &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; retorna xmedio &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; para := sim &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim se &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; se para é diferente de sim então &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; se (fmedio*fmin) &lt; 0 então &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; max := xmedio &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fmax := fmedio &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; j := j + 1 &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim se &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; senão &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; min := xmedio &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fmin := fmedio &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; j := j + 1 &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim senão &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim se &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim enquanto &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; se j &gt;= it então &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; 'O método não convergiu para este número de iterações' &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim se &lt;br&gt;
        fim se </traducao>
    <traducao xml:lang="en-us"/>
  </sentenca>
  <sentenca xml:id="EQNL_AJUDAb">
    <traducao xml:lang="pt-br">
        &lt;ul&gt;
        &lt;li&gt;Os arquivos devem estar no formato .txt.&lt;/li&gt; &lt;br&gt;
        &lt;li&gt;Cada linha deve conter apenas &lt;b&gt;um&lt;/b&gt; valor, na seguinte ordem: &lt;/li&gt; &lt;br&gt; 
        &lt;li&gt; &lt;b&gt; Arquivo de dados &lt;/b&gt;
        &lt;br&gt;
        &lt;br&gt; 1ª linha: '0' (zero) para calcular o método em um polinômio ou '1' para calcular o método em uma função qualquer. &lt;br&gt;
        &lt;br&gt; 2ª linha: caso a entrada seja através de um polinômio, digite o grau dele, senão, a função do problema, no &lt;a href=javascript:winopen('funcoesphp.php')&gt;formato&lt;/a&gt; reconhecido pelo programa. &lt;br&gt;
        &lt;br&gt; A partir da 3ª linha: coeficientes do polinômio para o caso polinomial, a partir do coeficiente que acompanha a variável de maior grau. Caso contrário, ignorar esta etapa.&lt;br&gt;
        &lt;br&gt; Em seguida: erro relativo para o resultado. &lt;br&gt;
        &lt;br&gt; Em seguida: número de iterações. &lt;br&gt;
        &lt;br&gt; Nas duas últimas linhas: valor de int1 e int2 (intervalo [int1,int2] da resposta). &lt;br&gt;
        &lt;br&gt;
        &lt;li&gt; &lt;b&gt; Arquivo de resposta &lt;/b&gt;
        &lt;br&gt;
        &lt;br&gt; 1ª linha: 0 caso o método não tenha convergido, ou 1 caso contrário. &lt;br&gt;
        &lt;br&gt; 2ª linha: Valor da resposta, caso haja. &lt;br&gt;
        &lt;br&gt; 3ª linha: Número de iterações, caso haja resposta. &lt;br&gt;
        &lt;/ul&gt;
    </traducao>
    <traducao xml:lang="en-us"/>
  </sentenca>
  <sentenca xml:id="EQNL_EXEc_01">
    <traducao xml:lang="pt-br">Polinômio de grau 3, com erro relativo de 0.00001</traducao>
    <traducao xml:lang="en-us"/>
  </sentenca>
  <sentenca xml:id="EQNL_ALGORITMOc">
    <traducao xml:lang="pt-br">
        &lt;b&gt;Variáveis: &lt;/b&gt; &lt;br&gt;&lt;br&gt; 
        Auxiliares: &lt;br&gt;
        i, j (contadores), derivada, para, resx0, resx1 &lt;br&gt;&lt;br&gt;
        De entrada: &lt;br&gt;
        deg (grau do polinômio) e coef (vetor de coeficientes do polinômio) ou uma função de entrada qualquer, x0 (estimativa inicial), it (número de iterações), error (margem de erro da resposta)  &lt;br&gt;&lt;br&gt;
        De saída: &lt;br&gt;
        x1 (quando o método convergir para uma solução)&lt;br&gt;&lt;br&gt;
        &lt;b&gt;Algoritmo: &lt;/b&gt; &lt;br&gt;&lt;br&gt; 
        para := não &lt;br&gt;
        resx0 := valor da função no ponto x0 &lt;br&gt;
        se resx0 = 0 então &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; 'O zero encontrado é exato' &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; retorna x0 &lt;br&gt;
        fim se &lt;br&gt;
        senão &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; enquanto (j &lt; it) e (para diferente de sim) então &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; derivada := valor da derivada no ponto x0 &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; se módulo(derivada) &gt;= error então &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; resx0 := valor da função no ponto x0 &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; x1 := x0-(resx0/derivada) &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; aux := máximo de(1,módulo(x1)) &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; err := módulo(resx0/derivada) / aux &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; resx1 := valor da função no ponto x1 &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; se err&lt;error então &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; 'O método convergiu' &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; retorna x1 &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; para := sim &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim se &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; se resx1=0 então &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; 'O zero encontrado é exato' &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; retorna x1 &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; para := sim &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim se &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; se para é diferente de sim então &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; x0 := x1 &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; j := j + 1 &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim se &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim se &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; senão &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; 'O denominador anula-se durante o processo utilizando estes valores iniciais' &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; para := sim &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim senão &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim enquanto &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; se j &gt;= it  &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; 'O método não convergiu para este número de iterações' &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim se  &lt;br&gt;
        fim senão </traducao>
    <traducao xml:lang="en-us"/>
  </sentenca>
  <sentenca xml:id="EQNL_AJUDAc">
    <traducao xml:lang="pt-br">
        &lt;ul&gt;
        &lt;li&gt;Os arquivos devem estar no formato .txt.&lt;/li&gt; &lt;br&gt;
        &lt;li&gt;Cada linha deve conter apenas &lt;b&gt;um&lt;/b&gt; valor, na seguinte ordem: &lt;/li&gt; &lt;br&gt;
        &lt;li&gt; &lt;b&gt; Arquivo de dados &lt;/b&gt;
        &lt;br&gt;
        &lt;br&gt; 1ª linha: '0' (zero) para calcular o método em um polinômio ou '1' para calcular o método em uma função qualquer. &lt;br&gt;
        &lt;br&gt; 2ª linha: caso a entrada seja através de um polinômio, digite o grau dele, senão, a função do problema, no &lt;a href=javascript:winopen('funcoesphp.php')&gt;formato&lt;/a&gt; reconhecido pelo programa. &lt;br&gt;
        &lt;br&gt; A partir da 3ª linha: coeficientes do polinômio para o caso polinomial, a partir do coeficiente que acompanha a variável de maior grau. Caso contrário, ignorar esta etapa.&lt;br&gt;
        &lt;br&gt; Em seguida: erro relativo para o resultado. &lt;br&gt;
        &lt;br&gt; Em seguida: número de iterações. &lt;br&gt;
        &lt;br&gt; Na última linha: valor de x0 (estimativa inicial). &lt;br&gt;
        &lt;br&gt;
        &lt;li&gt; &lt;b&gt; Arquivo de resposta &lt;/b&gt;
        &lt;br&gt;
        &lt;br&gt; 1ª linha: 0 caso o método não tenha convergido, ou 1 caso contrário. &lt;br&gt;
        &lt;br&gt; 2ª linha: Valor da resposta, caso haja. &lt;br&gt;
        &lt;br&gt; 3ª linha: Número de iterações, caso haja resposta. &lt;br&gt;
        &lt;/ul&gt;
    </traducao>
    <traducao xml:lang="en-us"/>
  </sentenca>
  <sentenca xml:id="GAUSS_MSG_01">
    <traducao xml:lang="pt-br">Eliminação de Gauss</traducao>
    <traducao xml:lang="en-us">Gauss Elimination</traducao>
  </sentenca>
  <sentenca xml:id="GAUSS_MSG_02">
    <traducao xml:lang="pt-br">Sistemas de Equações Algébricas Lineares</traducao>
    <traducao xml:lang="en-us">System of Linear Algebraic Equation</traducao>
  </sentenca>
  <sentenca xml:id="GAUSS_MSG_03a">
    <traducao xml:lang="pt-br">Eliminação de Gauss - Sem pivoteamento</traducao>
    <traducao xml:lang="en-us">Gauss Elimination - Without pivoting</traducao>
  </sentenca>
  <sentenca xml:id="GAUSS_MSG_03b">
    <traducao xml:lang="pt-br">Eliminação de Gauss - Com pivoteamento parcial</traducao>
    <traducao xml:lang="en-us">Gauss Elimination - With partial pivoting</traducao>
  </sentenca>
  <sentenca xml:id="GAUSS_MSG_03c">
    <traducao xml:lang="pt-br">Eliminação de Gauss - Com pivoteamento total</traducao>
    <traducao xml:lang="en-us">Gauss Elimination - With maximal pivoting</traducao>
  </sentenca>
  <sentenca xml:id="GAUSS_MSG_04">
    <traducao xml:lang="pt-br">Dimensão (número de variáveis): </traducao>
    <traducao xml:lang="en-us">Dimension (number of variables): </traducao>
  </sentenca>
  <sentenca xml:id="GAUSS_MSG_05">
    <traducao xml:lang="pt-br">Sistema</traducao>
    <traducao xml:lang="en-us">System</traducao>
  </sentenca>
  <sentenca xml:id="GAUSS_MSG_06">
    <traducao xml:lang="pt-br">Solução retirada do arquivo: </traducao>
    <traducao xml:lang="en-us">Extracted solution of the arquive </traducao>
  </sentenca>
  <sentenca xml:id="GAUSS_MSG_07">
    <traducao xml:lang="pt-br">Matriz A</traducao>
    <traducao xml:lang="en-us">Matrix A</traducao>
  </sentenca>
  <sentenca xml:id="GAUSS_MSG_08">
    <traducao xml:lang="pt-br">Triangularização</traducao>
    <traducao xml:lang="en-us">Forward elimination</traducao>
  </sentenca>
  <sentenca xml:id="GAUSS_MSG_09">
    <traducao xml:lang="pt-br">&lt;b&gt;Erro: &lt;/b&gt;Um dos pivôs anulou-se durante o processo de triangularização. Tente usar outro método.</traducao>
    <traducao xml:lang="en-us">&lt;b&gt;Error: &lt;/b&gt;One of the pivots was annulled during the forward elimination process.  Try to use another method.</traducao>
  </sentenca>
  <sentenca xml:id="GAUSS_MSG_09a">
    <traducao xml:lang="pt-br">Testar o método de Gauss com pivoteamento parcial  </traducao>
    <traducao xml:lang="en-us">Test the Gauss method with partial pivoting</traducao>
  </sentenca>
  <sentenca xml:id="GAUSS_MSG_10">
    <traducao xml:lang="pt-br">Testar o método de Gauss com pivoteamento total  </traducao>
    <traducao xml:lang="en-us">Test the Gauss method with maximal pivoting</traducao>
  </sentenca>
  <sentenca xml:id="GAUSS_MSG_11">
    <traducao xml:lang="pt-br">Passo </traducao>
    <traducao xml:lang="en-us">Step</traducao>
  </sentenca>
  <sentenca xml:id="GAUSS_MSG_12">
    <traducao xml:lang="pt-br">Matriz Triangular Superior</traducao>
    <traducao xml:lang="en-us">Upper triangular matrix</traducao>
  </sentenca>
  <sentenca xml:id="GAUSS_MSG_13">
    <traducao xml:lang="pt-br">Sistema Resultante</traducao>
    <traducao xml:lang="en-us">Resultant system</traducao>
  </sentenca>
  <sentenca xml:id="GAUSS_MSG_14">
    <traducao xml:lang="pt-br">Retrosubstituição</traducao>
    <traducao xml:lang="en-us">Back substitution</traducao>
  </sentenca>
  <sentenca xml:id="GAUSS_MSG_15">
    <traducao xml:lang="pt-br">Solução obtida do programa: </traducao>
    <traducao xml:lang="en-us">Gotten solution of the program </traducao>
  </sentenca>
  <sentenca xml:id="GAUSS_MSG_16">
    <traducao xml:lang="pt-br">Solução obtida do arquivo: </traducao>
    <traducao xml:lang="en-us">Gotten solution of the archive: </traducao>
  </sentenca>
  <sentenca xml:id="GAUSS_MSG_17">
    <traducao xml:lang="pt-br"> troca </traducao>
    <traducao xml:lang="en-us"> changes with </traducao>
  </sentenca>
  <sentenca xml:id="GAUSS_MSG_18">
    <traducao xml:lang="pt-br">'Clique Aqui'</traducao>
    <traducao xml:lang="en-us">'Click here'</traducao>
  </sentenca>
  <sentenca xml:id="GAUSS_MSG_19">
    <traducao xml:lang="pt-br">O sistema possui infinitas soluções. Uma solução possível é apresentada a seguir.</traducao>
    <traducao xml:lang="en-us">The system has infinite solutions. A possible solution is presented.</traducao>
  </sentenca>
  <sentenca xml:id="GAUSS_MSG_20">
    <traducao xml:lang="pt-br">O sistema não possui uma solução. Tente outro sistema.</traducao>
    <traducao xml:lang="en-us">The system has no solution. Try another system.</traducao>
  </sentenca>
  <sentenca xml:id="GAUSS_EXEa_01">
    <traducao xml:lang="pt-br">Sistema de dimensão 3</traducao>
    <traducao xml:lang="en-us">System of dimension 3</traducao>
  </sentenca>
  <sentenca xml:id="GAUSS_EXEa_02">
    <traducao xml:lang="pt-br">Sistema de dimensão 4</traducao>
    <traducao xml:lang="en-us">System of dimension 4</traducao>
  </sentenca>
  <sentenca xml:id="GAUSS_EXEa_03">
    <traducao xml:lang="pt-br">Sistema de dimensão 8</traducao>
    <traducao xml:lang="en-us">System of dimension 8</traducao>
  </sentenca>
  <sentenca xml:id="GAUSS_ALGORITMOa">
    <traducao xml:lang="pt-br">
        &lt;b&gt;Variáveis: &lt;/b&gt; &lt;br&gt;&lt;br&gt; 
        Auxiliares: &lt;br&gt;
        i, j, k (contadores), M (matriz) &lt;br&gt;&lt;br&gt;
        De entrada: &lt;br&gt;
        dim (dimensão da matriz) e A (matriz, tal que seja de dimensão dim x dim+1, onde a última coluna armazena o valor de b, para o sistema A x = b)  &lt;br&gt;&lt;br&gt;
        De saída: &lt;br&gt;
        VetX (vetor - quando há solução)&lt;br&gt;&lt;br&gt;
        &lt;b&gt;Algoritmo: &lt;/b&gt; &lt;br&gt;&lt;br&gt; 
        função triangularização (A,dim)  &lt;br&gt; 
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; para k de 0 a dim-2 faça &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; para i de k+1 a dim-1 faça &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; se A&lt;sub&gt;&lt;font size=2&gt;k,k&lt;/font&gt;&lt;/sub&gt; = 0 então &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; pivô se anula &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; parar o método &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim se &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; M&lt;sub&gt;&lt;font size=2&gt;i,k&lt;/font&gt;&lt;/sub&gt; := M&lt;sub&gt;&lt;font size=2&gt;i,k&lt;/font&gt;&lt;/sub&gt; - A&lt;sub&gt;&lt;font size=2&gt;i,k&lt;/font&gt;&lt;/sub&gt;/A&lt;sub&gt;&lt;font size=2&gt;k,k&lt;/font&gt;&lt;/sub&gt; &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; para j de 0 a dim faça &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; A&lt;sub&gt;&lt;font size=2&gt;i,j&lt;/font&gt;&lt;/sub&gt; := A&lt;sub&gt;&lt;font size=2&gt;i,j&lt;/font&gt;&lt;/sub&gt; + M&lt;sub&gt;&lt;font size=2&gt;i,k&lt;/font&gt;&lt;/sub&gt; * A&lt;sub&gt;&lt;font size=2&gt;k,j&lt;/font&gt;&lt;/sub&gt; &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim para &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim para &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim para &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; retorna A &lt;br&gt;
        fim função &lt;br&gt; &lt;br&gt;
        função retrosubstituição (B,dim)  &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; se B&lt;sub&gt;&lt;font size=2&gt;dim-1,dim-1&lt;/font&gt;&lt;/sub&gt; = 0 então &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; se B&lt;sub&gt;&lt;font size=2&gt;dim-1,dim&lt;/font&gt;&lt;/sub&gt; = 0  então // sistema tem infinitas soluções &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; VetX&lt;sub&gt;&lt;font size=2&gt;dim-1&lt;/font&gt;&lt;/sub&gt; := 1 &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; para k de dim-2 a 0 faça &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; VetX&lt;sub&gt;&lt;font size=2&gt;k&lt;/font&gt;&lt;/sub&gt; := B&lt;sub&gt;&lt;font size=2&gt;k,dim&lt;/font&gt;&lt;/sub&gt; &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; para i de k+1 a dim-1 faça &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; VetX&lt;sub&gt;&lt;font size=2&gt;k&lt;/font&gt;&lt;/sub&gt; := VetX&lt;sub&gt;&lt;font size=2&gt;k&lt;/font&gt;&lt;/sub&gt; - B&lt;sub&gt;&lt;font size=2&gt;k,i&lt;/font&gt;&lt;/sub&gt; * VetX&lt;sub&gt;&lt;font size=2&gt;i&lt;/font&gt;&lt;/sub&gt; &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim para &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; VetX&lt;sub&gt;&lt;font size=2&gt;k&lt;/font&gt;&lt;/sub&gt; := VetX&lt;sub&gt;&lt;font size=2&gt;k&lt;/font&gt;&lt;/sub&gt; / B&lt;sub&gt;&lt;font size=2&gt;k,k&lt;/font&gt;&lt;/sub&gt; &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim para &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; senão // sistema não possui solução &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; parar o método &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim se   &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; senão // sistema possui solução única &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; VetX&lt;sub&gt;&lt;font size=2&gt;dim-1&lt;/font&gt;&lt;/sub&gt; := B&lt;sub&gt;&lt;font size=2&gt;dim-1,dim&lt;/font&gt;&lt;/sub&gt; / B&lt;sub&gt;&lt;font size=2&gt;dim-1,dim-1&lt;/font&gt;&lt;/sub&gt; &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; para k de dim-2 a 0 faça &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; VetX&lt;sub&gt;&lt;font size=2&gt;k&lt;/font&gt;&lt;/sub&gt; := B&lt;sub&gt;&lt;font size=2&gt;k,dim&lt;/font&gt;&lt;/sub&gt; &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; para i de k+1 a dim-1 faça &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; VetX&lt;sub&gt;&lt;font size=2&gt;k&lt;/font&gt;&lt;/sub&gt; := VetX&lt;sub&gt;&lt;font size=2&gt;k&lt;/font&gt;&lt;/sub&gt; - B&lt;sub&gt;&lt;font size=2&gt;k,i&lt;/font&gt;&lt;/sub&gt; * VetX&lt;sub&gt;&lt;font size=2&gt;i&lt;/font&gt;&lt;/sub&gt; &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim para &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; VetX&lt;sub&gt;&lt;font size=2&gt;k&lt;/font&gt;&lt;/sub&gt; := VetX&lt;sub&gt;&lt;font size=2&gt;k&lt;/font&gt;&lt;/sub&gt; / B&lt;sub&gt;&lt;font size=2&gt;k,k&lt;/font&gt;&lt;/sub&gt; &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim para &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim se &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; retorna VetX &lt;br&gt;
        fim função &lt;br&gt; &lt;br&gt;
        VetX := retrossubstituição (triangularização(A,dim),dim) </traducao>
    <traducao xml:lang="en-us"/>
  </sentenca>
  <sentenca xml:id="GAUSS_ALGORITMOb">
    <traducao xml:lang="pt-br">
        &lt;b&gt;Variáveis: &lt;/b&gt; &lt;br&gt;&lt;br&gt; 
        Auxiliares: &lt;br&gt;
        i, j, k, l, cont (contadores), indice e aux2 (para troca de linha), M (matriz) &lt;br&gt;&lt;br&gt;
        De entrada: &lt;br&gt;
        dim (dimensão da matriz) e A (matriz, tal que seja de dimensão dim x dim+1, onde a última coluna armazena o valor de b, para o sistema A x = b)  &lt;br&gt;&lt;br&gt;
        De saída: &lt;br&gt;
        VetX (vetor - quando há solução)&lt;br&gt;&lt;br&gt;
        &lt;b&gt;Algoritmo: &lt;/b&gt; &lt;br&gt;&lt;br&gt; 
        função triangularização (A,dim)  &lt;br&gt; 
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; para k de 0 a dim-2 faça &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; para i de k+1 a dim-1 faça &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; se A&lt;sub&gt;&lt;font size=2&gt;k,k&lt;/font&gt;&lt;/sub&gt; = 0 então //pivô se anula &lt;br&gt; 
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; maior := módulo(A&lt;sub&gt;&lt;font size=2&gt;k,k&lt;/font&gt;&lt;/sub&gt;) &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; para cont de k+1 a dim-1 faça &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; //encontra elemento de maior valor absoluto na k-ésima coluna &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; se módulo(A&lt;sub&gt;&lt;font size=2&gt;cont,k&lt;/font&gt;&lt;/sub&gt;) &gt; maior então &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; maior := módulo(A&lt;sub&gt;&lt;font size=2&gt;cont,k&lt;/font&gt;&lt;/sub&gt;) &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; indice := cont &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim se &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim para &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; para l de 0 a dim faça //troca de linha &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; aux2 := A&lt;sub&gt;&lt;font size=2&gt;k,l&lt;/font&gt;&lt;/sub&gt; &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; A&lt;sub&gt;&lt;font size=2&gt;k,l&lt;/font&gt;&lt;/sub&gt; := A&lt;sub&gt;&lt;font size=2&gt;indice,l&lt;/font&gt;&lt;/sub&gt; &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; A&lt;sub&gt;&lt;font size=2&gt;indice,l&lt;/font&gt;&lt;/sub&gt; := aux2 &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim para &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim se &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; M&lt;sub&gt;&lt;font size=2&gt;i,k&lt;/font&gt;&lt;/sub&gt; := M&lt;sub&gt;&lt;font size=2&gt;i,k&lt;/font&gt;&lt;/sub&gt; - A&lt;sub&gt;&lt;font size=2&gt;i,k&lt;/font&gt;&lt;/sub&gt;/A&lt;sub&gt;&lt;font size=2&gt;k,k&lt;/font&gt;&lt;/sub&gt; &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; para j de 0 a dim faça &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; A&lt;sub&gt;&lt;font size=2&gt;i,j&lt;/font&gt;&lt;/sub&gt; := A&lt;sub&gt;&lt;font size=2&gt;i,j&lt;/font&gt;&lt;/sub&gt; + M&lt;sub&gt;&lt;font size=2&gt;i,k&lt;/font&gt;&lt;/sub&gt; * A&lt;sub&gt;&lt;font size=2&gt;k,j&lt;/font&gt;&lt;/sub&gt; &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim para &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim para &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim para &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; retorna A &lt;br&gt;
        fim função &lt;br&gt; &lt;br&gt;
        função retrosubstituição (B,dim)  &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; se B&lt;sub&gt;&lt;font size=2&gt;dim-1,dim-1&lt;/font&gt;&lt;/sub&gt; = 0 então &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; se B&lt;sub&gt;&lt;font size=2&gt;dim-1,dim&lt;/font&gt;&lt;/sub&gt; = 0  então // sistema tem infinitas soluções &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; VetX&lt;sub&gt;&lt;font size=2&gt;dim-1&lt;/font&gt;&lt;/sub&gt; := 1 &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; para k de dim-2 a 0 faça &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; VetX&lt;sub&gt;&lt;font size=2&gt;k&lt;/font&gt;&lt;/sub&gt; := B&lt;sub&gt;&lt;font size=2&gt;k,dim&lt;/font&gt;&lt;/sub&gt; &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; para i de k+1 a dim-1 faça &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; VetX&lt;sub&gt;&lt;font size=2&gt;k&lt;/font&gt;&lt;/sub&gt; := VetX&lt;sub&gt;&lt;font size=2&gt;k&lt;/font&gt;&lt;/sub&gt; - B&lt;sub&gt;&lt;font size=2&gt;k,i&lt;/font&gt;&lt;/sub&gt; * VetX&lt;sub&gt;&lt;font size=2&gt;i&lt;/font&gt;&lt;/sub&gt; &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim para &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; VetX&lt;sub&gt;&lt;font size=2&gt;k&lt;/font&gt;&lt;/sub&gt; := VetX&lt;sub&gt;&lt;font size=2&gt;k&lt;/font&gt;&lt;/sub&gt; / B&lt;sub&gt;&lt;font size=2&gt;k,k&lt;/font&gt;&lt;/sub&gt; &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim para &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; senão // sistema não possui solução &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; parar o método &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim se   &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; senão // sistema possui solução única &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; VetX&lt;sub&gt;&lt;font size=2&gt;dim-1&lt;/font&gt;&lt;/sub&gt; := B&lt;sub&gt;&lt;font size=2&gt;dim-1,dim&lt;/font&gt;&lt;/sub&gt; / B&lt;sub&gt;&lt;font size=2&gt;dim-1,dim-1&lt;/font&gt;&lt;/sub&gt; &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; para k de dim-2 a 0 faça &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; VetX&lt;sub&gt;&lt;font size=2&gt;k&lt;/font&gt;&lt;/sub&gt; := B&lt;sub&gt;&lt;font size=2&gt;k,dim&lt;/font&gt;&lt;/sub&gt; &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; para i de k+1 a dim-1 faça &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; VetX&lt;sub&gt;&lt;font size=2&gt;k&lt;/font&gt;&lt;/sub&gt; := VetX&lt;sub&gt;&lt;font size=2&gt;k&lt;/font&gt;&lt;/sub&gt; - B&lt;sub&gt;&lt;font size=2&gt;k,i&lt;/font&gt;&lt;/sub&gt; * VetX&lt;sub&gt;&lt;font size=2&gt;i&lt;/font&gt;&lt;/sub&gt; &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim para &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; VetX&lt;sub&gt;&lt;font size=2&gt;k&lt;/font&gt;&lt;/sub&gt; := VetX&lt;sub&gt;&lt;font size=2&gt;k&lt;/font&gt;&lt;/sub&gt; / B&lt;sub&gt;&lt;font size=2&gt;k,k&lt;/font&gt;&lt;/sub&gt; &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim para &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim se &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; retorna VetX &lt;br&gt;
        fim função &lt;br&gt; &lt;br&gt;
        VetX := retrossubstituição (triangularização(A,dim),dim) </traducao>
    <traducao xml:lang="en-us"/>
  </sentenca>
  <sentenca xml:id="GAUSS_EXEc_01">
    <traducao xml:lang="pt-br">Sistema de dimensão 4</traducao>
    <traducao xml:lang="en-us"/>
  </sentenca>
  <sentenca xml:id="GAUSS_ALGORITMOc">
    <traducao xml:lang="pt-br">
        &lt;b&gt;Variáveis: &lt;/b&gt; &lt;br&gt;&lt;br&gt; 
        Auxiliares: &lt;br&gt;
        i, j, k, l, cont1, cont2 (contadores), indice1, indice2 e aux2 (para troca de linha), M (matriz) &lt;br&gt;&lt;br&gt;
        De entrada: &lt;br&gt;
        dim (dimensão da matriz) e A (matriz, tal que seja de dimensão dim x dim+1, onde a última coluna armazena o valor de b, para o sistema A x = b)  &lt;br&gt;&lt;br&gt;
        De saída: &lt;br&gt;
        VetX (vetor - quando há solução)&lt;br&gt;&lt;br&gt;
        &lt;b&gt;Algoritmo: &lt;/b&gt; &lt;br&gt;&lt;br&gt; 
        função triangularização (A,dim)  &lt;br&gt; 
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; para k de 0 a dim-2 faça &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; para i de k+1 a dim-1 faça &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; se A&lt;sub&gt;&lt;font size=2&gt;k,k&lt;/font&gt;&lt;/sub&gt; = 0 então //pivô se anula &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; maior := módulo(A&lt;sub&gt;&lt;font size=2&gt;k,k&lt;/font&gt;&lt;/sub&gt;) &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; para cont1 de k+1 a dim-1 faça &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; para cont2 de k+1 a dim-1 faça &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; se módulo(A&lt;sub&gt;&lt;font size=2&gt;cont1,cont2&lt;/font&gt;&lt;/sub&gt;) &gt; maior então &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; maior := módulo(A&lt;sub&gt;&lt;font size=2&gt;cont1,cont2&lt;/font&gt;&lt;/sub&gt;) &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; indice1 := cont1 &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; indice2 := cont2 &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim se &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim para &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim para &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; para l de 0 a dim faça { //troca de linha &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; aux2 := A&lt;sub&gt;&lt;font size=2&gt;k,l&lt;/font&gt;&lt;/sub&gt; &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; A&lt;sub&gt;&lt;font size=2&gt;k,l&lt;/font&gt;&lt;/sub&gt; := A&lt;sub&gt;&lt;font size=2&gt;indice1,l&lt;/font&gt;&lt;/sub&gt; &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; A&lt;sub&gt;&lt;font size=2&gt;indice1,l&lt;/font&gt;&lt;/sub&gt; := aux2 &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim para &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; para l de 0 a dim faça { //troca de linha &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; aux2 := A&lt;sub&gt;&lt;font size=2&gt;l,k&lt;/font&gt;&lt;/sub&gt; &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; A&lt;sub&gt;&lt;font size=2&gt;l,k&lt;/font&gt;&lt;/sub&gt; := A&lt;sub&gt;&lt;font size=2&gt;l,indice2&lt;/font&gt;&lt;/sub&gt; &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; A&lt;sub&gt;&lt;font size=2&gt;l,indice2&lt;/font&gt;&lt;/sub&gt; := aux2 &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim para &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim se &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; M&lt;sub&gt;&lt;font size=2&gt;i,k&lt;/font&gt;&lt;/sub&gt; := M&lt;sub&gt;&lt;font size=2&gt;i,k&lt;/font&gt;&lt;/sub&gt; - A&lt;sub&gt;&lt;font size=2&gt;i,k&lt;/font&gt;&lt;/sub&gt;/A&lt;sub&gt;&lt;font size=2&gt;k,k&lt;/font&gt;&lt;/sub&gt; &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; para j de 0 a dim faça &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; A&lt;sub&gt;&lt;font size=2&gt;i,j&lt;/font&gt;&lt;/sub&gt; := A&lt;sub&gt;&lt;font size=2&gt;i,j&lt;/font&gt;&lt;/sub&gt; + M&lt;sub&gt;&lt;font size=2&gt;i,k&lt;/font&gt;&lt;/sub&gt; * A&lt;sub&gt;&lt;font size=2&gt;k,j&lt;/font&gt;&lt;/sub&gt; &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim para &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim para &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim para &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; retorna A &lt;br&gt;
        fim função &lt;br&gt; &lt;br&gt;
        função retrosubstituição (B,dim)  &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; se B&lt;sub&gt;&lt;font size=2&gt;dim-1,dim-1&lt;/font&gt;&lt;/sub&gt; = 0 então &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; se B&lt;sub&gt;&lt;font size=2&gt;dim-1,dim&lt;/font&gt;&lt;/sub&gt; = 0  então // sistema tem infinitas soluções &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; VetX&lt;sub&gt;&lt;font size=2&gt;dim-1&lt;/font&gt;&lt;/sub&gt; := 1 &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; para k de dim-2 a 0 faça &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; VetX&lt;sub&gt;&lt;font size=2&gt;k&lt;/font&gt;&lt;/sub&gt; := B&lt;sub&gt;&lt;font size=2&gt;k,dim&lt;/font&gt;&lt;/sub&gt; &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; para i de k+1 a dim-1 faça &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; VetX&lt;sub&gt;&lt;font size=2&gt;k&lt;/font&gt;&lt;/sub&gt; := VetX&lt;sub&gt;&lt;font size=2&gt;k&lt;/font&gt;&lt;/sub&gt; - B&lt;sub&gt;&lt;font size=2&gt;k,i&lt;/font&gt;&lt;/sub&gt; * VetX&lt;sub&gt;&lt;font size=2&gt;i&lt;/font&gt;&lt;/sub&gt; &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim para &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; VetX&lt;sub&gt;&lt;font size=2&gt;k&lt;/font&gt;&lt;/sub&gt; := VetX&lt;sub&gt;&lt;font size=2&gt;k&lt;/font&gt;&lt;/sub&gt; / B&lt;sub&gt;&lt;font size=2&gt;k,k&lt;/font&gt;&lt;/sub&gt; &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim para &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; senão // sistema não possui solução &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; parar o método &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim se   &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; senão // sistema possui solução única &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; VetX&lt;sub&gt;&lt;font size=2&gt;dim-1&lt;/font&gt;&lt;/sub&gt; := B&lt;sub&gt;&lt;font size=2&gt;dim-1,dim&lt;/font&gt;&lt;/sub&gt; / B&lt;sub&gt;&lt;font size=2&gt;dim-1,dim-1&lt;/font&gt;&lt;/sub&gt; &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; para k de dim-2 a 0 faça &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; VetX&lt;sub&gt;&lt;font size=2&gt;k&lt;/font&gt;&lt;/sub&gt; := B&lt;sub&gt;&lt;font size=2&gt;k,dim&lt;/font&gt;&lt;/sub&gt; &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; para i de k+1 a dim-1 faça &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; VetX&lt;sub&gt;&lt;font size=2&gt;k&lt;/font&gt;&lt;/sub&gt; := VetX&lt;sub&gt;&lt;font size=2&gt;k&lt;/font&gt;&lt;/sub&gt; - B&lt;sub&gt;&lt;font size=2&gt;k,i&lt;/font&gt;&lt;/sub&gt; * VetX&lt;sub&gt;&lt;font size=2&gt;i&lt;/font&gt;&lt;/sub&gt; &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim para &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; VetX&lt;sub&gt;&lt;font size=2&gt;k&lt;/font&gt;&lt;/sub&gt; := VetX&lt;sub&gt;&lt;font size=2&gt;k&lt;/font&gt;&lt;/sub&gt; / B&lt;sub&gt;&lt;font size=2&gt;k,k&lt;/font&gt;&lt;/sub&gt; &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim para &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim se &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; retorna VetX &lt;br&gt;
        fim função &lt;br&gt; &lt;br&gt;
        VetX := retrossubstituição (triangularização(A,dim),dim) </traducao>
    <traducao xml:lang="en-us"/>
  </sentenca>
  <sentenca xml:id="GAUSS_AJUDA">
    <traducao xml:lang="pt-br">
        &lt;ul&gt;
        &lt;li&gt;Os arquivos devem estar no formato .txt.&lt;/li&gt; &lt;br&gt;
        &lt;li&gt;Cada linha deve conter apenas &lt;b&gt;um&lt;/b&gt; valor, na seguinte ordem: &lt;/li&gt; &lt;br&gt;
        &lt;li&gt; &lt;b&gt; Arquivo de dados &lt;/b&gt;
        &lt;br&gt;
        &lt;br&gt; 1ª linha: dimensão da matriz A. &lt;br&gt;
        &lt;br&gt; A partir da 2ª linha: elementos da matriz A, a partir da primeira linha. Ao final de cada linha, inserir o valor do vetor B, tal que A x = B. &lt;br&gt;
        &lt;br&gt;
        &lt;li&gt; &lt;b&gt; Arquivo de resposta &lt;/b&gt;
        &lt;br&gt;
        &lt;br&gt; A partir da 1ª linha: elementos do vetor resposta. &lt;br&gt;
        &lt;/ul&gt;
    </traducao>
    <traducao xml:lang="en-us"/>
  </sentenca>
  <sentenca xml:id="GAUSS_SEIDEL_MSG_01">
    <traducao xml:lang="pt-br">Método iterativo de Gauss-Seidel</traducao>
    <traducao xml:lang="en-us">Iterative Gauss-Seidel method</traducao>
  </sentenca>
  <sentenca xml:id="GAUSS_SEIDEL_MSG_02">
    <traducao xml:lang="pt-br">Sistemas de Equações Algébricas Lineares</traducao>
    <traducao xml:lang="en-us">System of Linear Algebraic Equation</traducao>
  </sentenca>
  <sentenca xml:id="GAUSS_SEIDEL_MSG_03">
    <traducao xml:lang="pt-br">Gauss-Seidel</traducao>
    <traducao xml:lang="en-us">Gauss-Seidel</traducao>
  </sentenca>
  <sentenca xml:id="GAUSS_SEIDEL_MSG_04">
    <traducao xml:lang="pt-br">Dimensão (número de variáveis): </traducao>
    <traducao xml:lang="en-us">Dimension (number of variables): </traducao>
  </sentenca>
  <sentenca xml:id="GAUSS_SEIDEL_MSG_05">
    <traducao xml:lang="pt-br">Número máximo de iterações: </traducao>
    <traducao xml:lang="en-us">Maximum number of iterations: </traducao>
  </sentenca>
  <sentenca xml:id="GAUSS_SEIDEL_MSG_06">
    <traducao xml:lang="pt-br">Precisão desejada (digite o valor de k para 10&lt;sup&gt;-&lt;font size=2&gt;k&lt;/sup&gt;&lt;/font&gt;&amp;nbsp): </traducao>
    <traducao xml:lang="en-us">Desired precision (Type the value of k for the precision 10&lt;sup&gt;-&lt;font size=2&gt;k&lt;/sup&gt;&lt;/font&gt;&amp;nbsp): </traducao>
  </sentenca>
  <sentenca xml:id="GAUSS_SEIDEL_MSG_07">
    <traducao xml:lang="pt-br">Precisão desejada (valor de k para 10&lt;sup&gt;-&lt;font size=2&gt;k&lt;/sup&gt;&lt;/font&gt;&amp;nbsp): </traducao>
    <traducao xml:lang="en-us">Desired precision (value of k for the precision 10&lt;sup&gt;-&lt;font size=2&gt;k&lt;/sup&gt;&lt;/font&gt;&amp;nbsp): </traducao>
  </sentenca>
  <sentenca xml:id="GAUSS_SEIDEL_MSG_08">
    <traducao xml:lang="pt-br">Aproximações de x&lt;sub&gt;&lt;font size=1&gt;i&lt;/sub&gt;&lt;/font&gt;&lt;/font&gt;: </traducao>
    <traducao xml:lang="en-us">Approaches of x&lt;sub&gt;&lt;font size=1&gt;i&lt;/sub&gt;&lt;/font&gt;&lt;/font&gt;: </traducao>
  </sentenca>
  <sentenca xml:id="GAUSS_SEIDEL_MSG_09">
    <traducao xml:lang="pt-br">Solução retirada do arquivo</traducao>
    <traducao xml:lang="en-us">Extracted solution of the archive</traducao>
  </sentenca>
  <sentenca xml:id="GAUSS_SEIDEL_MSG_10">
    <traducao xml:lang="pt-br">O método não convergiu.</traducao>
    <traducao xml:lang="en-us">The method did not converge.</traducao>
  </sentenca>
  <sentenca xml:id="GAUSS_SEIDEL_MSG_11">
    <traducao xml:lang="pt-br">Solução obtida do arquivo</traducao>
    <traducao xml:lang="en-us">Gotten solution of the archive</traducao>
  </sentenca>
  <sentenca xml:id="GAUSS_SEIDEL_MSG_12">
    <traducao xml:lang="pt-br">Não é possível utilizar o método de Gauss-Seidel no sistema dado</traducao>
    <traducao xml:lang="en-us">It is not possible to use Gauss-Seidel method in this system</traducao>
  </sentenca>
  <sentenca xml:id="GAUSS_SEIDEL_MSG_13">
    <traducao xml:lang="pt-br">pois o determinante da matriz do sistema é nulo.</traducao>
    <traducao xml:lang="en-us">because de determinant of the matrix is null.</traducao>
  </sentenca>
  <sentenca xml:id="GAUSS_SEIDEL_MSG_14">
    <traducao xml:lang="pt-br">Clique em 'Início' para inserir uma matriz válida.</traducao>
    <traducao xml:lang="en-us">Click in 'Beginning' to insert a valid matrix.</traducao>
  </sentenca>
  <sentenca xml:id="GAUSS_SEIDEL_MSG_15">
    <traducao xml:lang="pt-br">Não é possível utilizar o método de Gauss-Seidel no sistema dado</traducao>
    <traducao xml:lang="en-us">It is not possible to use Gauss-Seidel method in this system</traducao>
  </sentenca>
  <sentenca xml:id="GAUSS_SEIDEL_MSG_16">
    <traducao xml:lang="pt-br">pois pelo menos um dos elementos da matriz principal do sistema é nulo.</traducao>
    <traducao xml:lang="en-us">because at least one of the elements of the principal matrix of the system is null.</traducao>
  </sentenca>
  <sentenca xml:id="GAUSS_SEIDEL_MSG_17">
    <traducao xml:lang="pt-br">Resultados Parciais</traducao>
    <traducao xml:lang="en-us">Partial Results</traducao>
  </sentenca>
  <sentenca xml:id="GAUSS_SEIDEL_MSG_18">
    <traducao xml:lang="pt-br"> iteração:</traducao>
    <traducao xml:lang="en-us"> iteration:</traducao>
  </sentenca>
  <sentenca xml:id="GAUSS_SEIDEL_MSG_19">
    <traducao xml:lang="pt-br">O método convergiu para </traducao>
    <traducao xml:lang="en-us">The method converged to </traducao>
  </sentenca>
  <sentenca xml:id="GAUSS_SEIDEL_MSG_20">
    <traducao xml:lang="pt-br"> iterações.</traducao>
    <traducao xml:lang="en-us"> iterations.</traducao>
  </sentenca>
  <sentenca xml:id="GAUSS_SEIDEL_MSG_21">
    <traducao xml:lang="pt-br">Solução obtida do programa</traducao>
    <traducao xml:lang="en-us">Gotten solution of the program</traducao>
  </sentenca>
  <sentenca xml:id="GAUSS_SEIDEL_MSG_22">
    <traducao xml:lang="pt-br">'Testar outras aproximações para x'</traducao>
    <traducao xml:lang="en-us">'Test other approaches to x'</traducao>
  </sentenca>
  <sentenca xml:id="GAUSS_SEIDEL_MSG_23">
    <traducao xml:lang="pt-br">Sistema</traducao>
    <traducao xml:lang="en-us">System</traducao>
  </sentenca>
  <sentenca xml:id="GAUSS_SEIDEL_MSG_24">
    <traducao xml:lang="pt-br">Precisão desejada: </traducao>
    <traducao xml:lang="en-us">Desired precision: </traducao>
  </sentenca>
  <sentenca xml:id="GAUSS_SEIDEL_MSG_25">
    <traducao xml:lang="pt-br">Aviso: a matriz não é diagonal dominante, nem satisfaz o critério de Sassenfeld. Não há garantias de convergência do método.</traducao>
    <traducao xml:lang="en-us">Warning: the matrix is not diagonally dominant, and also does not meet the Sassenfeld criteria. The method's convergence is not garanteed.</traducao>
  </sentenca>
  <sentenca xml:id="GAUSS_SEIDEL_EXE_01">
    <traducao xml:lang="pt-br">Sistema de dimensão 4, precisão de 4 casas decimais, e número máximo de iterações = 100</traducao>
    <traducao xml:lang="en-us">System of dimension 4, precision of 10&lt;sup&gt;-4&lt;/sup&gt;, and maximum number of iterations = 100</traducao>
  </sentenca>
  <sentenca xml:id="GAUSS_SEIDEL_ALGORITMO">
    <traducao xml:lang="pt-br">
        &lt;b&gt;Variáveis: &lt;/b&gt; &lt;br&gt;&lt;br&gt; 
        Auxiliares: &lt;br&gt;
        i, j (contadores), vtemp, vtd, (vetores), dif, num, chegou, pode, aux &lt;br&gt;&lt;br&gt;
        De entrada: &lt;br&gt;
        dim (dimensão da matriz), A e T (matriz e vetor, para o sistema A x = T), t (precisão da resposta), k (número de iterações)  &lt;br&gt;&lt;br&gt;
        De saída: &lt;br&gt;
        vtx (vetor - quando há solução)&lt;br&gt;&lt;br&gt;
        &lt;b&gt;Algoritmo: &lt;/b&gt; &lt;br&gt;&lt;br&gt; 
        aux := 1 &lt;br&gt;
        num := 10 &lt;br&gt;
        para i de 1 a t faça &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; aux := aux*num &lt;br&gt;
        fim para &lt;br&gt;
        num := (1/aux) &lt;br&gt;
        pode := 1 &lt;br&gt;
        se determinante (A) = o então &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; pode := 0 &lt;br&gt;
        fim se &lt;br&gt;
        para i de 0 a dim-1 faça &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; se A&lt;sub&gt;&lt;font size=2&gt;i,i&lt;/font&gt;&lt;/sub&gt; = 0 então &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; pode := -1 &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim se &lt;br&gt;
        fim para &lt;br&gt;
        vezes := 0 &lt;br&gt;
        se pode = 0 então &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; 'Não é possível executar o método pois o determinante da matriz do sistema é nulo.' &lt;br&gt;
        fim se &lt;br&gt;
        senao se pode = -1 então &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; 'Não é possível executar o método pois um dos elementos da diagonal principal da matriz do sistema é nulo.' &lt;br&gt;
        fim senão &lt;br&gt;
        para i de 1 a dim-1 faça &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; vtd&lt;sub&gt;&lt;font size=2&gt;i&lt;/font&gt;&lt;/sub&gt; := vtx&lt;sub&gt;&lt;font size=2&gt;i&lt;/font&gt;&lt;/sub&gt; &lt;br&gt;
        fim para &lt;br&gt;
        se pode = 1 então &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; enquanto (chegou é diferente de 1) e (vezes&lt;=k) faça &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; vezes := vezes + 1 &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; para i de 0 a dim-1 faça &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; para j de 0 a dim-1 faça &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; se i é diferente de j então &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; vtemp&lt;sub&gt;&lt;font size=2&gt;i&lt;/font&gt;&lt;/sub&gt; := vtemp&lt;sub&gt;&lt;font size=2&gt;i&lt;/font&gt;&lt;/sub&gt; + A&lt;sub&gt;&lt;font size=2&gt;i,j&lt;/font&gt;&lt;/sub&gt;*vtx&lt;sub&gt;&lt;font size=2&gt;j&lt;/font&gt;&lt;/sub&gt; &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim se &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim para &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; vtemp&lt;sub&gt;&lt;font size=2&gt;i&lt;/font&gt;&lt;/sub&gt; := vtemp&lt;sub&gt;&lt;font size=2&gt;i&lt;/font&gt;&lt;/sub&gt; - T&lt;sub&gt;&lt;font size=2&gt;i&lt;/font&gt;&lt;/sub&gt; &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; vtemp&lt;sub&gt;&lt;font size=2&gt;i&lt;/font&gt;&lt;/sub&gt; := vtemp&lt;sub&gt;&lt;font size=2&gt;i&lt;/font&gt;&lt;/sub&gt; * (-1/A&lt;sub&gt;&lt;font size=2&gt;i,i&lt;/font&gt;&lt;/sub&gt;) &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; vtx&lt;sub&gt;&lt;font size=2&gt;i&lt;/font&gt;&lt;/sub&gt; := vtemp&lt;sub&gt;&lt;font size=2&gt;i&lt;/font&gt;&lt;/sub&gt; &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim para &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; chegou :=1 &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; para i de 0 a dim-1 faça &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; dif := módulo(vtd&lt;sub&gt;&lt;font size=2&gt;i&lt;/font&gt;&lt;/sub&gt;-vtemp&lt;sub&gt;&lt;font size=2&gt;i&lt;/font&gt;&lt;/sub&gt;) &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; se dif &gt; num então &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; chegou := 0 &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim se &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim para &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; para i de 0 a dim-1 faça &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; vtd&lt;sub&gt;&lt;font size=2&gt;i&lt;/font&gt;&lt;/sub&gt; := vtx&lt;sub&gt;&lt;font size=2&gt;i&lt;/font&gt;&lt;/sub&gt; &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; vtemp&lt;sub&gt;&lt;font size=2&gt;i&lt;/font&gt;&lt;/sub&gt; := 0 &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim para &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim enquanto &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; se chegou = 1 &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; retorna vtx &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim se &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; senão &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; 'O método não convergiu' &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim senão &lt;br&gt;
        fim se </traducao>
    <traducao xml:lang="en-us"/>
  </sentenca>
  <sentenca xml:id="GAUSS_SEIDEL_AJUDA">
    <traducao xml:lang="pt-br">
        &lt;ul&gt;
        &lt;li&gt;Os arquivos devem estar no formato .txt.&lt;/li&gt; &lt;br&gt;
        &lt;li&gt;Cada linha deve conter apenas &lt;b&gt;um&lt;/b&gt; valor, na seguinte ordem: &lt;/li&gt; &lt;br&gt;
        &lt;li&gt; &lt;b&gt; Arquivo de dados &lt;/b&gt;
        &lt;br&gt;
        &lt;br&gt; 1ª linha: dimensão da matriz A. &lt;br&gt;
        &lt;br&gt; 2ª linha: número de iterações. &lt;br&gt;
        &lt;br&gt; 3ª linha: valor k da precisão desejada (tal que precisão desejada = 10&lt;sup&gt;-k&lt;/sup&gt;. &lt;br&gt;
        &lt;br&gt; A partir da 4ª linha: elementos da matriz A, a partir da primeira linha. Ao final de cada linha, inserir o valor do vetor B, tal que A x = B. &lt;br&gt;
        &lt;br&gt; Em seguida: elementos do vetor de aproximação inicial. &lt;br&gt;   
        &lt;br&gt;
        &lt;li&gt; &lt;b&gt; Arquivo de resposta &lt;/b&gt;
        &lt;br&gt;
        &lt;br&gt; 1ª linha: 0 caso o método não tenha convergido, e 1 caso contrário. &lt;br&gt;
        &lt;br&gt; A partir da 2ª linha: elementos do vetor resposta, caso o método tenha convergido. &lt;br&gt;
        &lt;/ul&gt;
    </traducao>
    <traducao xml:lang="en-us"/>
  </sentenca>
  <sentenca xml:id="GRAFICO_MSG_01">
    <traducao xml:lang="pt-br">Pontos do problema</traducao>
    <traducao xml:lang="en-us">Points of the problem</traducao>
  </sentenca>
  <sentenca xml:id="GRAFICO_MSG_02">
    <traducao xml:lang="pt-br">Ponto interpolado</traducao>
    <traducao xml:lang="en-us">Interpolated point</traducao>
  </sentenca>
  <sentenca xml:id="GRAFICO_MSG_03">
    <traducao xml:lang="pt-br">Polinômio interpolador</traducao>
    <traducao xml:lang="en-us">Interpolating polynomia</traducao>
  </sentenca>
  <sentenca xml:id="GRAFICO_MSG_04">
    <traducao xml:lang="pt-br">Gráfico do polinômio</traducao>
    <traducao xml:lang="en-us">Function</traducao>
  </sentenca>
  <sentenca xml:id="GRAFICO_MSG_05">
    <traducao xml:lang="pt-br">Ajuste de dados</traducao>
    <traducao xml:lang="en-us">Data fitting</traducao>
  </sentenca>
  <sentenca xml:id="GRAFICO_MSG_06">
    <traducao xml:lang="pt-br">Função original</traducao>
    <traducao xml:lang="en-us">Original function</traducao>
  </sentenca>
  <sentenca xml:id="GRAFICO_MSG_07">
    <traducao xml:lang="pt-br">Função obtida pelo programa</traducao>
    <traducao xml:lang="en-us">Least-squares polynomial</traducao>
  </sentenca>
  <sentenca xml:id="INTNUM_MSG_01">
    <traducao xml:lang="pt-br">Integrais</traducao>
    <traducao xml:lang="en-us">Integration</traducao>
  </sentenca>
  <sentenca xml:id="INTNUM_MSG_02">
    <traducao xml:lang="pt-br">Integração numérica</traducao>
    <traducao xml:lang="en-us">Numeric integration</traducao>
  </sentenca>
  <sentenca xml:id="INTNUM_MSG_03a">
    <traducao xml:lang="pt-br">Método da Extrapolação de Richardson</traducao>
    <traducao xml:lang="en-us">Richardson's Extrapolation method</traducao>
  </sentenca>
  <sentenca xml:id="INTNUM_MSG_03b">
    <traducao xml:lang="pt-br">Método de Romberg</traducao>
    <traducao xml:lang="en-us">Romberg's method</traducao>
  </sentenca>
  <sentenca xml:id="INTNUM_MSG_03c">
    <traducao xml:lang="pt-br">Método de Simpson</traducao>
    <traducao xml:lang="en-us">Simpson's method</traducao>
  </sentenca>
  <sentenca xml:id="INTNUM_MSG_03d">
    <traducao xml:lang="pt-br">Método do trapézio</traducao>
    <traducao xml:lang="en-us">Trapezoidal method</traducao>
  </sentenca>
  <sentenca xml:id="INTNUM_MSG_04">
    <traducao xml:lang="pt-br">Digite a função </traducao>
    <traducao xml:lang="en-us">Type the function </traducao>
  </sentenca>
  <sentenca xml:id="INTNUM_MSG_06">
    <traducao xml:lang="pt-br">Digite os limites inferior e superior da integração: </traducao>
    <traducao xml:lang="en-us">Type the lower and upper limits of integration: </traducao>
  </sentenca>
  <sentenca xml:id="INTNUM_MSG_07">
    <traducao xml:lang="pt-br">Função dada: </traducao>
    <traducao xml:lang="en-us">Given function: </traducao>
  </sentenca>
  <sentenca xml:id="INTNUM_MSG_08">
    <traducao xml:lang="pt-br">Limite inferior (a): </traducao>
    <traducao xml:lang="en-us">Lower limit (a): </traducao>
  </sentenca>
  <sentenca xml:id="INTNUM_MSG_09">
    <traducao xml:lang="pt-br">Limite superior (b): </traducao>
    <traducao xml:lang="en-us">Upper limit (b): </traducao>
  </sentenca>
  <sentenca xml:id="INTNUM_MSG_10">
    <traducao xml:lang="pt-br">Resposta retirada do arquivo: </traducao>
    <traducao xml:lang="en-us">Extracted answer of the archive: </traducao>
  </sentenca>
  <sentenca xml:id="INTNUM_MSG_11">
    <traducao xml:lang="pt-br">Resultado da Integral = </traducao>
    <traducao xml:lang="en-us">Result of the integration = </traducao>
  </sentenca>
  <sentenca xml:id="INTNUM_MSG_14">
    <traducao xml:lang="pt-br">Resposta obtida do programa: </traducao>
    <traducao xml:lang="en-us">Gotten answer of the program: </traducao>
  </sentenca>
  <sentenca xml:id="INTNUM_MSG_15">
    <traducao xml:lang="pt-br">Resposta obtida do arquivo: </traducao>
    <traducao xml:lang="en-us">Gotten answer of the archive: </traducao>
  </sentenca>
  <sentenca xml:id="INTNUM_MSG_12a">
    <traducao xml:lang="pt-br">Informe um número par n de partições do intervalo:</traducao>
    <traducao xml:lang="en-us">Inform a pair number n of partitions of the interval:</traducao>
  </sentenca>
  <sentenca xml:id="INTNUM_MSG_13a">
    <traducao xml:lang="pt-br">Informe um número par m (onde m &gt; n) de partições do intervalo:</traducao>
    <traducao xml:lang="en-us">Inform a pair number m (where m &gt; n) of partitions of the interval:</traducao>
  </sentenca>
  <sentenca xml:id="INTNUM_MSG_16a">
    <traducao xml:lang="pt-br">Número de partições n: </traducao>
    <traducao xml:lang="en-us">Number of partitions n: </traducao>
  </sentenca>
  <sentenca xml:id="INTNUM_MSG_17a">
    <traducao xml:lang="pt-br">Número de partições m: </traducao>
    <traducao xml:lang="en-us">Number of partitions m: </traducao>
  </sentenca>
  <sentenca xml:id="INTNUM_ALGORITMOa">
    <traducao xml:lang="pt-br">
        &lt;b&gt;Variáveis: &lt;/b&gt; &lt;br&gt;&lt;br&gt; 
        Auxiliares: &lt;br&gt;
        i (contador), f e v (vetores), fa, fb, integ1, integ2, delta, sum &lt;br&gt;&lt;br&gt;
        De entrada: &lt;br&gt;
        função (na sintaxe reconhecida pelo programa), a e b (intervalo da integração), vn e vm (número de partições tal que vm &gt; vn e vm e vn sejam pares)  &lt;br&gt;&lt;br&gt;
        De saída: &lt;br&gt;
        resp (resultado da integral)&lt;br&gt;&lt;br&gt;
        &lt;b&gt;Algoritmo: &lt;/b&gt; &lt;br&gt;&lt;br&gt; 
        função simpson(a,b,vn,coef,deg) &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fa := valor da função no ponto x=a &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fb := valor da função no ponto x=b &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; delta := (b-a)/vn &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; para i de 0 a vn-2 faça &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; v&lt;sub&gt;&lt;font size=2&gt;i&lt;/font&gt;&lt;/sub&gt; := valor da função no ponto x=(a+(i+1)*delta) &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim para &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; sum := 0 &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; sum := fa+fb &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; para i de 0 a vn-2 faça &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; se (i+1) é par então &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; sum := sum+(2*v&lt;sub&gt;&lt;font size=2&gt;i&lt;/font&gt;&lt;/sub&gt;) &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim se &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; senão &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; sum := sum+(4*v&lt;sub&gt;&lt;font size=2&gt;i&lt;/font&gt;&lt;/sub&gt;) &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim para &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; aprox := ((b-a)/(3*vn))*sum &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; retorna aprox &lt;br&gt;
        fim função &lt;br&gt; &lt;br&gt;
        função richardson(a,b,vn,vm,coef,deg) &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; integ1 := simpson(a,b,vn,coef,deg) &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; integ2 := simpson(a,b,vm,coef,deg) &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; resp := integ2 + (vn&lt;sup&gt;4&lt;/sup&gt; / (vm&lt;sup&gt;4&lt;/sup&gt;-vn&lt;sup&gt;4&lt;/sup&gt;)) * (integ2-integ1) &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; retorna resp &lt;br&gt;
        fim função &lt;br&gt; &lt;br&gt; </traducao>
    <traducao xml:lang="en-us"/>
  </sentenca>
  <sentenca xml:id="INTNUM_AJUDAa">
    <traducao xml:lang="pt-br">
        &lt;ul&gt;
        &lt;li&gt;Os arquivos devem estar no formato .txt.&lt;/li&gt; &lt;br&gt;
        &lt;li&gt;Cada linha deve conter apenas &lt;b&gt;um&lt;/b&gt;, na seguinte ordem: &lt;/li&gt; &lt;br&gt;
        &lt;li&gt; &lt;b&gt; Arquivo de dados &lt;/b&gt;
        &lt;br&gt;
        &lt;br&gt; 1ª linha: função do problema, no &lt;a href=javascript:winopen('funcoesphp.php')&gt;formato&lt;/a&gt; reconhecido pelo programa. &lt;br&gt;
        &lt;br&gt; Em seguida: valores de a e b (intervalo [a,b]), respectivamente. &lt;br&gt;
        &lt;br&gt; Em seguida: número par de partições 'n'. &lt;br&gt;
        &lt;br&gt; Por fim: número par de partições 'm', maior que 'n'. &lt;br&gt;
        &lt;br&gt;
        &lt;li&gt; &lt;b&gt; Arquivo de resposta &lt;/b&gt;
        &lt;br&gt;
        &lt;br&gt; 1ª linha: resultado da integral. &lt;br&gt;
        &lt;/ul&gt;
    </traducao>
    <traducao xml:lang="en-us"/>
  </sentenca>
  <sentenca xml:id="INTNUM_MSG_12b">
    <traducao xml:lang="pt-br">Informe um número n de partições do intervalo:</traducao>
    <traducao xml:lang="en-us">Inform a number n of partitions of the interval:</traducao>
  </sentenca>
  <sentenca xml:id="INTNUM_MSG_13b">
    <traducao xml:lang="pt-br">Informe um número m (onde m &gt; n) de partições do intervalo:</traducao>
    <traducao xml:lang="en-us">Inform a number m (where m > n) of partitions of the interval:</traducao>
  </sentenca>
  <sentenca xml:id="INTNUM_MSG_16b">
    <traducao xml:lang="pt-br">Número de partições n: </traducao>
    <traducao xml:lang="en-us">Number of partitions n: </traducao>
  </sentenca>
  <sentenca xml:id="INTNUM_MSG_17b">
    <traducao xml:lang="pt-br">Número de partições m: </traducao>
    <traducao xml:lang="en-us">Number of partitions m: </traducao>
  </sentenca>
  <sentenca xml:id="INTNUM_ALGORITMOb">
    <traducao xml:lang="pt-br">
        &lt;b&gt;Variáveis: &lt;/b&gt; &lt;br&gt;&lt;br&gt; 
        Auxiliares: &lt;br&gt;
        i (contador), f e v (vetores), fa, fb, integ1, integ2, delta, sum &lt;br&gt;&lt;br&gt;
        De entrada: &lt;br&gt;
        função (na sintaxe reconhecida pelo programa), a e b (intervalo da integração), vn e vm (número de partições tal que vm &gt; vn)  &lt;br&gt;&lt;br&gt;
        De saída: &lt;br&gt;
        resp (resultado da integral)&lt;br&gt;&lt;br&gt;
        &lt;b&gt;Algoritmo: &lt;/b&gt; &lt;br&gt;&lt;br&gt; 
        função trapezio(funcao,a,b,vn) &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fa := valor da função no ponto x=a &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fb := valor da função no ponto x=b &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; delta := (b-a)/vn &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; para i de 0 a vn-2 faça &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; v&lt;sub&gt;&lt;font size=2&gt;i&lt;/font&gt;&lt;/sub&gt; := valor da função no ponto x=(a+(i+1)*delta) &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim para &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; sum := 0 &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; sum := fa+fb &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; para i de 0 a vn-2 faça &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; sum := sum+(2*v&lt;sub&gt;&lt;font size=2&gt;i&lt;/font&gt;&lt;/sub&gt;) &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim para &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; aprox := ((b-a)/(2*vn))*sum &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; retorna aprox &lt;br&gt;
        fim função &lt;br&gt; &lt;br&gt;
        função romberg(a,b,vn,vm,coef,deg) &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; integ1 := trapezio(a,b,vn,coef,deg) &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; integ2 := trapezio(a,b,vm,coef,deg) &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; resp := integ2 + (vn&lt;sup&gt;2&lt;/sup&gt;/(vm&lt;sup&gt;2&lt;/sup&gt;-vn&lt;sup&gt;2&lt;/sup&gt;)) * (integ2-integ1) &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; retorna resp &lt;br&gt;
        fim função </traducao>
    <traducao xml:lang="en-us"/>
  </sentenca>
  <sentenca xml:id="INTNUM_AJUDAb">
    <traducao xml:lang="pt-br">
        &lt;ul&gt;
        &lt;li&gt;Os arquivos devem estar no formato .txt.&lt;/li&gt; &lt;br&gt;
        &lt;li&gt;Cada linha deve conter apenas &lt;b&gt;um&lt;/b&gt;, na seguinte ordem: &lt;/li&gt; &lt;br&gt;
        &lt;li&gt; &lt;b&gt; Arquivo de dados &lt;/b&gt;
        &lt;br&gt;
        &lt;br&gt; 1ª linha: função do problema, no &lt;a href=javascript:winopen('funcoesphp.php')&gt;formato&lt;/a&gt; reconhecido pelo programa. &lt;br&gt;
        &lt;br&gt; Em seguida: valores de a e b (intervalo [a,b]), respectivamente. &lt;br&gt;
        &lt;br&gt; Em seguida: número de partições 'n'. &lt;br&gt;
        &lt;br&gt; Por fim: número de partições 'm', maior que 'n'. &lt;br&gt;
        &lt;br&gt;
        &lt;li&gt; &lt;b&gt; Arquivo de resposta &lt;/b&gt;
        &lt;br&gt;
        &lt;br&gt; 1ª linha: resultado da integral. &lt;br&gt;
        &lt;/ul&gt;
    </traducao>
    <traducao xml:lang="en-us"/>
  </sentenca>
  <sentenca xml:id="INTNUM_MSG_12c">
    <traducao xml:lang="pt-br">Informe um número par n de partições do intervalo:</traducao>
    <traducao xml:lang="en-us">Inform a pair number n of partitions of the interval:</traducao>
  </sentenca>
  <sentenca xml:id="INTNUM_MSG_16c">
    <traducao xml:lang="pt-br">Número de partições n: </traducao>
    <traducao xml:lang="en-us">Number of partitions n: </traducao>
  </sentenca>
  <sentenca xml:id="INTNUM_ALGORITMOc">
    <traducao xml:lang="pt-br">
        &lt;b&gt;Variáveis: &lt;/b&gt; &lt;br&gt;&lt;br&gt; 
        Auxiliares: &lt;br&gt;
        i (contador), f e v (vetores), fa, fb, delta, sum &lt;br&gt;&lt;br&gt;
        De entrada: &lt;br&gt;
        função (na sintaxe reconhecida pelo programa), a e b (intervalo da integração), vn (número de partições tal que vn seja par)  &lt;br&gt;&lt;br&gt;
        De saída: &lt;br&gt;
        aprox (resultado da integral)&lt;br&gt;&lt;br&gt;
        &lt;b&gt;Algoritmo: &lt;/b&gt; &lt;br&gt;&lt;br&gt; 
        função simpson(a,b,vn,coef,deg) &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fa := valor da função no ponto x=a &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fb := valor da função no ponto x=b &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; delta := (b-a)/vn &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; para i de 0 a vn-2 faça &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; v&lt;sub&gt;&lt;font size=2&gt;i&lt;/font&gt;&lt;/sub&gt; := valor da função no ponto x=(a+(i+1)*delta) &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim para &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; sum := 0 &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; sum := fa+fb &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; para i de 0 a vn-2 faça &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; se (i+1) é par então &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; sum := sum+(2*v&lt;sub&gt;&lt;font size=2&gt;i&lt;/font&gt;&lt;/sub&gt;) &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim se &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; senão &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; sum := sum+(4*v&lt;sub&gt;&lt;font size=2&gt;i&lt;/font&gt;&lt;/sub&gt;) &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim para &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; aprox := ((b-a)/(3*vn))*sum &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; retorna aprox &lt;br&gt;
        fim função &lt;br&gt; &lt;br&gt; </traducao>
    <traducao xml:lang="en-us"/>
  </sentenca>
  <sentenca xml:id="INTNUM_AJUDAc">
    <traducao xml:lang="pt-br">
        &lt;ul&gt;
        &lt;li&gt;Os arquivos devem estar no formato .txt.&lt;/li&gt; &lt;br&gt;
        &lt;li&gt;Cada linha deve conter apenas &lt;b&gt;um&lt;/b&gt;, na seguinte ordem: &lt;/li&gt; &lt;br&gt;
        &lt;li&gt; &lt;b&gt; Arquivo de dados &lt;/b&gt;
        &lt;br&gt;
        &lt;br&gt; 1ª linha: função do problema, no &lt;a href=javascript:winopen('funcoesphp.php')&gt;formato&lt;/a&gt; reconhecido pelo programa. &lt;br&gt;
        &lt;br&gt; Em seguida: valores de a e b (intervalo [a,b]), respectivamente. &lt;br&gt;
        &lt;br&gt; Em seguida: número par de partições 'n'. &lt;br&gt;
        &lt;br&gt;
        &lt;li&gt; &lt;b&gt; Arquivo de resposta &lt;/b&gt;
        &lt;br&gt;
        &lt;br&gt; 1ª linha: resultado da integral. &lt;br&gt;
        &lt;/ul&gt;
    </traducao>
    <traducao xml:lang="en-us"/>
  </sentenca>
  <sentenca xml:id="INTNUM_MSG_12d">
    <traducao xml:lang="pt-br">Informe um número n de partições do intervalo:</traducao>
    <traducao xml:lang="en-us">Inform a number n of partitions of the interval:</traducao>
  </sentenca>
  <sentenca xml:id="INTNUM_MSG_16d">
    <traducao xml:lang="pt-br">Número de partições n: </traducao>
    <traducao xml:lang="en-us">Number of partitions n: </traducao>
  </sentenca>
  <sentenca xml:id="INTNUM_ALGORITMOd">
    <traducao xml:lang="pt-br">
        &lt;b&gt;Variáveis: &lt;/b&gt; &lt;br&gt;&lt;br&gt; 
        Auxiliares: &lt;br&gt;
        i (contador), f e v (vetores), fa, fb, delta, sum &lt;br&gt;&lt;br&gt;
        De entrada: &lt;br&gt;
        função (na sintaxe reconhecida pelo programa), a e b (intervalo da integração), vn (número de partições)  &lt;br&gt;&lt;br&gt;
        De saída: &lt;br&gt;
        aprox (resultado da integral)&lt;br&gt;&lt;br&gt;
        &lt;b&gt;Algoritmo: &lt;/b&gt; &lt;br&gt;&lt;br&gt; 
        função trapezio(a,b,vn,coef,deg) &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fa := valor da função no ponto x=a &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fb := valor da função no ponto x=b &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; delta := (b-a)/vn &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; para i de 0 a vn-2 faça &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; v&lt;sub&gt;&lt;font size=2&gt;i&lt;/font&gt;&lt;/sub&gt; := valor da função no ponto x=(a+(i+1)*delta) &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim para &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; sum := 0 &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; sum := fa+fb &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; para i de 0 a vn-2 faça &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; sum := sum+(2*v&lt;sub&gt;&lt;font size=2&gt;i&lt;/font&gt;&lt;/sub&gt;) &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim para &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; aprox := ((b-a)/(2*vn))*sum &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; retorna aprox &lt;br&gt;
        fim função &lt;br&gt; &lt;br&gt; </traducao>
    <traducao xml:lang="en-us"/>
  </sentenca>
  <sentenca xml:id="INTNUM_AJUDAd">
    <traducao xml:lang="pt-br">
        &lt;ul&gt;
        &lt;li&gt;Os arquivos devem estar no formato .txt.&lt;/li&gt; &lt;br&gt;
        &lt;li&gt;Cada linha deve conter apenas &lt;b&gt;um&lt;/b&gt;, na seguinte ordem: &lt;/li&gt; &lt;br&gt;
        &lt;li&gt; &lt;b&gt; Arquivo de dados &lt;/b&gt;
        &lt;br&gt;
        &lt;br&gt; 1ª linha: função do problema, no &lt;a href=javascript:winopen('funcoesphp.php')&gt;formato&lt;/a&gt; reconhecido pelo programa. &lt;br&gt;
        &lt;br&gt; Em seguida: valores de a e b (intervalo [a,b]), respectivamente. &lt;br&gt;
        &lt;br&gt; Em seguida: número de partições 'n'. &lt;br&gt;
        &lt;br&gt;
        &lt;li&gt; &lt;b&gt; Arquivo de resposta &lt;/b&gt;
        &lt;br&gt;
        &lt;br&gt; 1ª linha: resultado da integral. &lt;br&gt;
        &lt;/ul&gt;
    </traducao>
    <traducao xml:lang="en-us"/>
  </sentenca>
  <sentenca xml:id="INVERSA_MSG_01">
    <traducao xml:lang="pt-br">Inversão de Matrizes - por eliminação de Gauss</traducao>
    <traducao xml:lang="en-us">Inversion of Matrices - by Gauss Elimination</traducao>
  </sentenca>
  <sentenca xml:id="INVERSA_MSG_02">
    <traducao xml:lang="pt-br">Aritmética Matricial</traducao>
    <traducao xml:lang="en-us">Matricial Arithmetic</traducao>
  </sentenca>
  <sentenca xml:id="INVERSA_MSG_03">
    <traducao xml:lang="pt-br">Inversão</traducao>
    <traducao xml:lang="en-us">Inversion</traducao>
  </sentenca>
  <sentenca xml:id="INVERSA_MSG_04">
    <traducao xml:lang="pt-br">Dimensão: </traducao>
    <traducao xml:lang="en-us">Dimension: </traducao>
  </sentenca>
  <sentenca xml:id="INVERSA_MSG_05">
    <traducao xml:lang="pt-br">Matriz A</traducao>
    <traducao xml:lang="en-us">Matrix A</traducao>
  </sentenca>
  <sentenca xml:id="INVERSA_MSG_06">
    <traducao xml:lang="pt-br">Matriz B (A&lt;sup&gt;-1&lt;/sup&gt;) - Resposta obtida do arquivo:</traducao>
    <traducao xml:lang="en-us">Matrix B (A&lt;sup&gt;-1&lt;/sup&gt;) - Gotten answer of the archive:</traducao>
  </sentenca>
  <sentenca xml:id="INVERSA_MSG_07">
    <traducao xml:lang="pt-br">Matriz B (A&lt;sup&gt;-1&lt;/sup&gt;) - Resposta obtida do programa: </traducao>
    <traducao xml:lang="en-us">Matrix B (A&lt;sup&gt;-1&lt;/sup&gt;) - Gotten answer of the program: </traducao>
  </sentenca>
  <sentenca xml:id="INVERSA_ALGORITMO">
    <traducao xml:lang="pt-br">
        &lt;b&gt;Variáveis: &lt;/b&gt; &lt;br&gt;&lt;br&gt; 
        Auxiliares: &lt;br&gt;
        i, j, k (contadores), t (vetor), p, B (matriz de dimensão dim x 2*dim) &lt;br&gt;&lt;br&gt;
        De entrada: &lt;br&gt;
        A (matriz), dim (dimensão da matriz) &lt;br&gt;&lt;br&gt;
        De saída: &lt;br&gt;
        B (matriz de dimensão dim x 2*dim, que corresponde à matriz identidade (primeira metade) a a matriz inversa (segunda metade)&lt;br&gt;&lt;br&gt;
        &lt;b&gt;Algoritmo: &lt;/b&gt; &lt;br&gt;&lt;br&gt; 
        para i de 0 a dim-1 faça &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; para j de 0 a 2*dim-1 faça &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; se i = j-dim então &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; B&lt;sub&gt;&lt;font size=2&gt;i,j&lt;/font&gt;&lt;/sub&gt; := 1 &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim se &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; else { &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; se j&lt;dim então &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; B&lt;sub&gt;&lt;font size=2&gt;i,j&lt;/font&gt;&lt;/sub&gt; := A&lt;sub&gt;&lt;font size=2&gt;i,j&lt;/font&gt;&lt;/sub&gt; &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim se &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; senão &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; B&lt;sub&gt;&lt;font size=2&gt;i,j&lt;/font&gt;&lt;/sub&gt; := 0 &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim else &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim else &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim para j &lt;br&gt;
        fim para i &lt;br&gt;
        para k de 0 a dim-1 faça &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; p := B&lt;sub&gt;&lt;font size=2&gt;k,k&lt;/font&gt;&lt;/sub&gt; &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; para i de 0 a dim faça &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; t&lt;sub&gt;&lt;font size=2&gt;i&lt;/font&gt;&lt;/sub&gt; := B&lt;sub&gt;&lt;font size=2&gt;i,k&lt;/font&gt;&lt;/sub&gt; &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim para i &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; para j de k a 2*dim-1 faça &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; B&lt;sub&gt;&lt;font size=2&gt;k,j&lt;/font&gt;&lt;/sub&gt; := B&lt;sub&gt;&lt;font size=2&gt;k,j&lt;/font&gt;&lt;/sub&gt;/p &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; para i de 0 a dim-1 faça &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; se k diferente de i então &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; B&lt;sub&gt;&lt;font size=2&gt;i,j&lt;/font&gt;&lt;/sub&gt; := B&lt;sub&gt;&lt;font size=2&gt;i,j&lt;/font&gt;&lt;/sub&gt;-t&lt;sub&gt;&lt;font size=2&gt;i&lt;/font&gt;&lt;/sub&gt;*B&lt;sub&gt;&lt;font size=2&gt;k,j&lt;/font&gt;&lt;/sub&gt; &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim se &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim for i &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim for j &lt;br&gt;
        fim for k &lt;br&gt;
        retorna B </traducao>
    <traducao xml:lang="en-us"/>
  </sentenca>
  <sentenca xml:id="INVERSA_AJUDA">
    <traducao xml:lang="pt-br">
        &lt;ul&gt;
        &lt;li&gt;Os arquivos devem estar no formato .txt.&lt;/li&gt; &lt;br&gt;
        &lt;li&gt;Cada linha deve conter apenas &lt;b&gt;um&lt;/b&gt; valor, na seguinte ordem: &lt;/li&gt; &lt;br&gt; 
        &lt;li&gt; &lt;b&gt; Arquivo de dados &lt;/b&gt;
        &lt;br&gt;
        &lt;br&gt; 1ª linha: dimensão da matriz A. &lt;br&gt;
        &lt;br&gt; A partir da 2ª linha: elementos da matriz A, em ordem crescente de coluna e linha. &lt;br&gt;
        &lt;br&gt;
        &lt;li&gt; &lt;b&gt; Arquivo de resposta &lt;/b&gt;
        &lt;br&gt;
        &lt;br&gt; A partir da 1ª linha: elementos da matriz B, em ordem crescente de coluna e linha. &lt;br&gt;
        &lt;/ul&gt;
    </traducao>
    <traducao xml:lang="en-us"/>
  </sentenca>
  <sentenca xml:id="JACOBI_MSG_01">
    <traducao xml:lang="pt-br">Método iterativo de Jacobi</traducao>
    <traducao xml:lang="en-us">Iterative Jacobi method</traducao>
  </sentenca>
  <sentenca xml:id="JACOBI_MSG_02">
    <traducao xml:lang="pt-br">Sistemas de Equações Algébricas Lineares</traducao>
    <traducao xml:lang="en-us">System of Linear Algebraic Equation</traducao>
  </sentenca>
  <sentenca xml:id="JACOBI_MSG_03">
    <traducao xml:lang="pt-br">Jacobi</traducao>
    <traducao xml:lang="en-us">Jacobi</traducao>
  </sentenca>
  <sentenca xml:id="JACOBI_MSG_04">
    <traducao xml:lang="pt-br">Dimensão (número de variáveis): </traducao>
    <traducao xml:lang="en-us">Dimension (number of variables): </traducao>
  </sentenca>
  <sentenca xml:id="JACOBI_MSG_05">
    <traducao xml:lang="pt-br">Número máximo de iterações: </traducao>
    <traducao xml:lang="en-us">Maximum number of iterations: </traducao>
  </sentenca>
  <sentenca xml:id="JACOBI_MSG_06">
    <traducao xml:lang="pt-br">Precisão desejada (digite o valor de k para 10&lt;sup&gt;-&lt;font size=2&gt;k&lt;/sup&gt;&lt;/font&gt;&amp;nbsp): </traducao>
    <traducao xml:lang="en-us">Desired precision (Type the value of k for the precision 10&lt;sup&gt;-&lt;font size=2&gt;k&lt;/sup&gt;&lt;/font&gt;&amp;nbsp): </traducao>
  </sentenca>
  <sentenca xml:id="JACOBI_MSG_07">
    <traducao xml:lang="pt-br">Precisão desejada (valor de k para 10&lt;sup&gt;-&lt;font size=2&gt;k&lt;/sup&gt;&lt;/font&gt;&amp;nbsp): </traducao>
    <traducao xml:lang="en-us">Desired precision (value of k for the precision 10&lt;sup&gt;-&lt;font size=2&gt;k&lt;/sup&gt;&lt;/font&gt;&amp;nbsp): </traducao>
  </sentenca>
  <sentenca xml:id="JACOBI_MSG_08">
    <traducao xml:lang="pt-br">Aproximações de x&lt;sub&gt;&lt;font size=1&gt;i&lt;/sub&gt;&lt;/font&gt;&lt;/font&gt;: </traducao>
    <traducao xml:lang="en-us">Approaches of x&lt;sub&gt;&lt;font size=1&gt;i&lt;/sub&gt;&lt;/font&gt;&lt;/font>&gt; </traducao>
  </sentenca>
  <sentenca xml:id="JACOBI_MSG_09">
    <traducao xml:lang="pt-br">Solução retirada do arquivo</traducao>
    <traducao xml:lang="en-us">Extracted solution of the archive</traducao>
  </sentenca>
  <sentenca xml:id="JACOBI_MSG_10">
    <traducao xml:lang="pt-br">O método não convergiu.</traducao>
    <traducao xml:lang="en-us">The method did not converge."</traducao>
  </sentenca>
  <sentenca xml:id="JACOBI_MSG_11">
    <traducao xml:lang="pt-br">Solução obtida do arquivo</traducao>
    <traducao xml:lang="en-us">Gotten solution of the archive</traducao>
  </sentenca>
  <sentenca xml:id="JACOBI_MSG_12">
    <traducao xml:lang="pt-br">Não é possível utilizar o método de Jacobi no sistema dado</traducao>
    <traducao xml:lang="en-us">It is not possible to use Gauss-Seidel method in this system</traducao>
  </sentenca>
  <sentenca xml:id="JACOBI_MSG_13">
    <traducao xml:lang="pt-br">pois o determinante da matriz do sistema é nulo.</traducao>
    <traducao xml:lang="en-us">because de determinant of the matrix is null.</traducao>
  </sentenca>
  <sentenca xml:id="JACOBI_MSG_14">
    <traducao xml:lang="pt-br">Clique em 'Início' para inserir uma matriz válida.</traducao>
    <traducao xml:lang="en-us">Click in 'Beginning' to insert a valid matrix.</traducao>
  </sentenca>
  <sentenca xml:id="JACOBI_MSG_15">
    <traducao xml:lang="pt-br">Não é possível utilizar o método de Jacobi no sistema dado</traducao>
    <traducao xml:lang="en-us">It is not possible to use Gauss-Seidel method in this system</traducao>
  </sentenca>
  <sentenca xml:id="JACOBI_MSG_16">
    <traducao xml:lang="pt-br">pois pelo menos um dos elementos da matriz principal do sistema é nulo.</traducao>
    <traducao xml:lang="en-us">because at least one of the elements of the principal matrix of the system is null.</traducao>
  </sentenca>
  <sentenca xml:id="JACOBI_MSG_17">
    <traducao xml:lang="pt-br">Resultados Parciais</traducao>
    <traducao xml:lang="en-us">Partial Results</traducao>
  </sentenca>
  <sentenca xml:id="JACOBI_MSG_18">
    <traducao xml:lang="pt-br"> iteração:</traducao>
    <traducao xml:lang="en-us"> iteration:</traducao>
  </sentenca>
  <sentenca xml:id="JACOBI_MSG_19">
    <traducao xml:lang="pt-br">O método convergiu para </traducao>
    <traducao xml:lang="en-us">The method converged to </traducao>
  </sentenca>
  <sentenca xml:id="JACOBI_MSG_20">
    <traducao xml:lang="pt-br"> iterações.</traducao>
    <traducao xml:lang="en-us"> iterations.</traducao>
  </sentenca>
  <sentenca xml:id="JACOBI_MSG_21">
    <traducao xml:lang="pt-br">Solução obtida do programa</traducao>
    <traducao xml:lang="en-us">Gotten solution of the program</traducao>
  </sentenca>
  <sentenca xml:id="JACOBI_MSG_22">
    <traducao xml:lang="pt-br">'Testar outras aproximações para x'</traducao>
    <traducao xml:lang="en-us">'Test other approaches to x'</traducao>
  </sentenca>
  <sentenca xml:id="JACOBI_MSG_23">
    <traducao xml:lang="pt-br">Sistema</traducao>
    <traducao xml:lang="en-us">System</traducao>
  </sentenca>
  <sentenca xml:id="JACOBI_MSG_24">
    <traducao xml:lang="pt-br">Precisão desejada: </traducao>
    <traducao xml:lang="en-us">Desired precision: </traducao>
  </sentenca>
  <sentenca xml:id="JACOBI_MSG_25">
    <traducao xml:lang="pt-br">O problema não satisfaz o critério das colunas, não há garantias de convergencia do método.</traducao>
    <traducao xml:lang="en-us">The problem does not meet the columns criteria, the method's convergence is not garanteed</traducao>
  </sentenca>
  <sentenca xml:id="JACOBI_ALGORITMO">
    <traducao xml:lang="pt-br">
        &lt;b&gt;Variáveis: &lt;/b&gt; &lt;br&gt;&lt;br&gt; 
        Auxiliares: &lt;br&gt;
        i, j (contadores), vtemp (vetor), dif, num, chegou, pode, aux &lt;br&gt;&lt;br&gt;
        De entrada: &lt;br&gt;
        dim (dimensão da matriz), A e T (matriz e vetor, para o sistema A x = T), t (precisão da resposta), k (número de iterações)  &lt;br&gt;&lt;br&gt;
        De saída: &lt;br&gt;
        vtx (vetor - quando há solução)&lt;br&gt;&lt;br&gt;
        &lt;b&gt;Algoritmo: &lt;/b&gt; &lt;br&gt;&lt;br&gt; 
        aux := 1 &lt;br&gt;
        num := 10 &lt;br&gt;
        para i de 1 a t faça &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; aux := aux*num &lt;br&gt;
        fim para &lt;br&gt;
        num := (1/aux) &lt;br&gt;
        pode := 1 &lt;br&gt;
        se determinante (A) = o então &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; pode := 0 &lt;br&gt;
        fim se &lt;br&gt;
        para i de 0 a dim-1 faça &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; se A&lt;sub&gt;&lt;font size=2&gt;i,i&lt;/font&gt;&lt;/sub&gt; = 0 então &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; pode := -1 &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim se &lt;br&gt;
        fim para &lt;br&gt;
        vezes := 0 &lt;br&gt;
        se pode = 0 então &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; 'Não é possível executar o método pois o determinante da matriz do sistema é nulo.' &lt;br&gt;
        fim se &lt;br&gt;
        senao se pode = -1 então &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; 'Não é possível executar o método pois um dos elementos da diagonal principal da matriz do sistema é nulo.' &lt;br&gt;
        fim senão &lt;br&gt;
        para i de 1 a dim-1 faça &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; vtd&lt;sub&gt;&lt;font size=2&gt;i&lt;/font&gt;&lt;/sub&gt; := vtx&lt;sub&gt;&lt;font size=2&gt;i&lt;/font&gt;&lt;/sub&gt; &lt;br&gt;
        fim para &lt;br&gt;
        se pode = 1 então &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; enquanto (chegou é diferente de 1) e (vezes&lt;=k) faça &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; vezes := vezes + 1 &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; para i de 0 a dim-1 faça &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; para j de 0 a dim-1 faça &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; se i é diferente de j então &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; vtemp&lt;sub&gt;&lt;font size=2&gt;i&lt;/font&gt;&lt;/sub&gt; := vtemp&lt;sub&gt;&lt;font size=2&gt;i&lt;/font&gt;&lt;/sub&gt; + A&lt;sub&gt;&lt;font size=2&gt;i,j&lt;/font&gt;&lt;/sub&gt;*vtx&lt;sub&gt;&lt;font size=2&gt;j&lt;/font&gt;&lt;/sub&gt; &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim se &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim para &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; vtemp&lt;sub&gt;&lt;font size=2&gt;i&lt;/font&gt;&lt;/sub&gt; := vtemp&lt;sub&gt;&lt;font size=2&gt;i&lt;/font&gt;&lt;/sub&gt; - T&lt;sub&gt;&lt;font size=2&gt;i&lt;/font&gt;&lt;/sub&gt; &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; vtemp&lt;sub&gt;&lt;font size=2&gt;i&lt;/font&gt;&lt;/sub&gt; := vtemp&lt;sub&gt;&lt;font size=2&gt;i&lt;/font&gt;&lt;/sub&gt; * (-1/A&lt;sub&gt;&lt;font size=2&gt;i,i&lt;/font&gt;&lt;/sub&gt;) &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; vtx&lt;sub&gt;&lt;font size=2&gt;i&lt;/font&gt;&lt;/sub&gt; := vtemp&lt;sub&gt;&lt;font size=2&gt;i&lt;/font&gt;&lt;/sub&gt; &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim para &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; chegou :=1 &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; para i de 0 a dim-1 faça &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; dif := módulo(vtx&lt;sub&gt;&lt;font size=2&gt;i&lt;/font&gt;&lt;/sub&gt;-vtemp&lt;sub&gt;&lt;font size=2&gt;i&lt;/font&gt;&lt;/sub&gt;) &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; se dif &gt; num então &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; chegou := 0 &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim se &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim para &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; para i de 0 a dim-1 faça &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; vtx&lt;sub&gt;&lt;font size=2&gt;i&lt;/font&gt;&lt;/sub&gt; := vtemp&lt;sub&gt;&lt;font size=2&gt;i&lt;/font&gt;&lt;/sub&gt; &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; vtemp&lt;sub&gt;&lt;font size=2&gt;i&lt;/font&gt;&lt;/sub&gt; := 0 &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim para &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim enquanto &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; se chegou = 1 &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; retorna vtx &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim se &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; senão &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; 'O método não convergiu' &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim senão &lt;br&gt;
        fim se </traducao>
    <traducao xml:lang="en-us"/>
  </sentenca>
  <sentenca xml:id="JACOBI_AJUDA">
    <traducao xml:lang="pt-br">
        &lt;ul&gt;
        &lt;li&gt;Os arquivos devem estar no formato .txt.&lt;/li&gt; &lt;br&gt;
        &lt;li&gt;Cada linha deve conter apenas &lt;b&gt;um&lt;/b&gt; valor, na seguinte ordem: &lt;/li&gt; &lt;br&gt;
        &lt;li&gt; &lt;b&gt; Arquivo de dados &lt;/b&gt;
        &lt;br&gt;
        &lt;br&gt; 1ª linha: dimensão da matriz A. &lt;br&gt;
        &lt;br&gt; 2ª linha: número de iterações. &lt;br&gt;
        &lt;br&gt; 3ª linha: valor k da precisão desejada (tal que precisão desejada = 10&lt;sup&gt;-k&lt;/sup&gt;. &lt;br&gt;
        &lt;br&gt; A partir da 4ª linha: elementos da matriz A, a partir da primeira linha. Ao final de cada linha, inserir o valor do vetor B, tal que A x = B. &lt;br&gt;
        &lt;br&gt; Em seguida: elementos do vetor de aproximação inicial. &lt;br&gt;   
        &lt;br&gt;
        &lt;li&gt; &lt;b&gt; Arquivo de resposta &lt;/b&gt;
        &lt;br&gt;
        &lt;br&gt; 1ª linha: 0 caso o método não tenha convergido, e 1 caso contrário. &lt;br&gt;
        &lt;br&gt; A partir da 2ª linha: elementos do vetor resposta, caso o método tenha convergido. &lt;br&gt;
        &lt;/ul&gt;
    </traducao>
    <traducao xml:lang="en-us"/>
  </sentenca>
  <sentenca xml:id="LAGRANGE_MSG_01">
    <traducao xml:lang="pt-br">Método de Lagrange</traducao>
    <traducao xml:lang="en-us">Lagrange Method</traducao>
  </sentenca>
  <sentenca xml:id="LAGRANGE_MSG_02">
    <traducao xml:lang="pt-br">Interpolação Polinomial</traducao>
    <traducao xml:lang="en-us">Polynomial Interpolation</traducao>
  </sentenca>
  <sentenca xml:id="LAGRANGE_MSG_03">
    <traducao xml:lang="pt-br">Lagrange</traducao>
    <traducao xml:lang="en-us">Lagrange</traducao>
  </sentenca>
  <sentenca xml:id="LAGRANGE_MSG_04">
    <traducao xml:lang="pt-br">Selecione uma opção para entrada de dados:</traducao>
    <traducao xml:lang="en-us">Select an option of problem:</traducao>
  </sentenca>
  <sentenca xml:id="LAGRANGE_MSG_05">
    <traducao xml:lang="pt-br">Caso discreto (através de um conjunto de pontos)</traducao>
    <traducao xml:lang="en-us">Discrete case (through a set of points)</traducao>
  </sentenca>
  <sentenca xml:id="LAGRANGE_MSG_06">
    <traducao xml:lang="pt-br">Caso contínuo (através de uma função e um intervalo)</traducao>
    <traducao xml:lang="en-us">Continuous case (through a function and a interval)</traducao>
  </sentenca>
  <sentenca xml:id="LAGRANGE_MSG_07">
    <traducao xml:lang="pt-br">Digite o número de pontos que serão dados como entrada: </traducao>
    <traducao xml:lang="en-us">Type the number of points that will be given as entry: </traducao>
  </sentenca>
  <sentenca xml:id="LAGRANGE_MSG_09">
    <traducao xml:lang="pt-br">Digite a função: </traducao>
    <traducao xml:lang="en-us">Type the function: </traducao>
  </sentenca>
  <sentenca xml:id="LAGRANGE_MSG_10">
    <traducao xml:lang="pt-br">Digite o intervalo em que a função será aproximada: </traducao>
    <traducao xml:lang="en-us">Type the interval where the function will be aproached: </traducao>
  </sentenca>
  <sentenca xml:id="LAGRANGE_MSG_11">
    <traducao xml:lang="pt-br">Tipo de distribuição dos </traducao>
    <traducao xml:lang="en-us">Type of distribution of the </traducao>
  </sentenca>
  <sentenca xml:id="LAGRANGE_MSG_12">
    <traducao xml:lang="pt-br"> pontos no intervalo </traducao>
    <traducao xml:lang="en-us"> points of the interval </traducao>
  </sentenca>
  <sentenca xml:id="LAGRANGE_MSG_13">
    <traducao xml:lang="pt-br">Distribuição uniforme</traducao>
    <traducao xml:lang="en-us">Uniform distribution</traducao>
  </sentenca>
  <sentenca xml:id="LAGRANGE_MSG_14">
    <traducao xml:lang="pt-br">Distribuição de Chebyshev</traducao>
    <traducao xml:lang="en-us">Chebyshev distribution</traducao>
  </sentenca>
  <sentenca xml:id="LAGRANGE_MSG_15">
    <traducao xml:lang="pt-br">Número de pontos:</traducao>
    <traducao xml:lang="en-us">Number of points:</traducao>
  </sentenca>
  <sentenca xml:id="LAGRANGE_MSG_16">
    <traducao xml:lang="pt-br">Grau do polinômio p(x): </traducao>
    <traducao xml:lang="en-us">Degree of the polynomial p(x) </traducao>
  </sentenca>
  <sentenca xml:id="LAGRANGE_MSG_17">
    <traducao xml:lang="pt-br">Função dada:</traducao>
    <traducao xml:lang="en-us">Given function:</traducao>
  </sentenca>
  <sentenca xml:id="LAGRANGE_MSG_18">
    <traducao xml:lang="pt-br">Intervalo </traducao>
    <traducao xml:lang="en-us">Interval </traducao>
  </sentenca>
  <sentenca xml:id="LAGRANGE_MSG_19">
    <traducao xml:lang="pt-br">Valores de (x , y):</traducao>
    <traducao xml:lang="en-us">Values of (x,y):</traducao>
  </sentenca>
  <sentenca xml:id="LAGRANGE_MSG_20">
    <traducao xml:lang="pt-br">Calcular p(x) para x= </traducao>
    <traducao xml:lang="en-us">Calculate p(x) to x= </traducao>
  </sentenca>
  <sentenca xml:id="LAGRANGE_MSG_21">
    <traducao xml:lang="pt-br">Resposta retirada do arquivo: </traducao>
    <traducao xml:lang="en-us">Extracted answer of the archive: </traducao>
  </sentenca>
  <sentenca xml:id="LAGRANGE_MSG_22">
    <traducao xml:lang="pt-br">Resposta obtida do programa: </traducao>
    <traducao xml:lang="en-us">Gotten answer of the program: </traducao>
  </sentenca>
  <sentenca xml:id="LAGRANGE_MSG_23">
    <traducao xml:lang="pt-br">Resposta obtida do arquivo: </traducao>
    <traducao xml:lang="en-us">Gotten answer of the archive: </traducao>
  </sentenca>
  <sentenca xml:id="LAGRANGE_MSG_24">
    <traducao xml:lang="pt-br">Fórmula de Chebyshev: </traducao>
    <traducao xml:lang="en-us">Chebyshev formula: </traducao>
  </sentenca>
  <sentenca xml:id="LAGRANGE_ALGORITMO">
    <traducao xml:lang="pt-br">
        &lt;b&gt;Variáveis: &lt;/b&gt; &lt;br&gt;&lt;br&gt; 
        Auxiliares: &lt;br&gt;
        i, k (contadores), l, divisor (vetores), grau &lt;br&gt;&lt;br&gt;
        De entrada: &lt;br&gt;
        n (número de pontos), X e Y (vetores), valor (ponto a ser interpolado)  &lt;br&gt;&lt;br&gt;
        De saída: &lt;br&gt;
        p (resultado da interpolação no ponto 'valor')&lt;br&gt;&lt;br&gt;
        &lt;b&gt;Algoritmo: &lt;/b&gt; &lt;br&gt;&lt;br&gt; 
        grau := n - 1 &lt;br&gt;
        para i de 0 a grau faça &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; l&lt;sub&gt;&lt;font size=2&gt;i&lt;/font&gt;&lt;/sub&gt; := 1 &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; divisor&lt;sub&gt;&lt;font size=2&gt;i&lt;/font&gt;&lt;/sub&gt; := 1 &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; para k de 0 a grau faça &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; se k é diferente de i então &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; divisor&lt;sub&gt;&lt;font size=2&gt;i&lt;/font&gt;&lt;/sub&gt; := divisor&lt;sub&gt;&lt;font size=2&gt;i&lt;/font&gt;&lt;/sub&gt; * X&lt;sub&gt;&lt;font size=2&gt;i&lt;/font&gt;&lt;/sub&gt;-X&lt;sub&gt;&lt;font size=2&gt;k&lt;/font&gt;&lt;/sub&gt; &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; l&lt;sub&gt;&lt;font size=2&gt;i&lt;/font&gt;&lt;/sub&gt; := l&lt;sub&gt;&lt;font size=2&gt;i&lt;/font&gt;&lt;/sub&gt; * (valor-X&lt;sub&gt;&lt;font size=2&gt;k&lt;/font&gt;&lt;/sub&gt;) / (X&lt;sub&gt;&lt;font size=2&gt;i&lt;/font&gt;&lt;/sub&gt;-X&lt;sub&gt;&lt;font size=2&gt;k&lt;/font&gt;&lt;/sub&gt;) &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim se &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim para &lt;br&gt;
        fim para  &lt;br&gt;
        p := 0 &lt;br&gt;
        para i de 0 a grau faça &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; p = p + l&lt;sub&gt;&lt;font size=2&gt;i&lt;/font&gt;&lt;/sub&gt;*Y&lt;sub&gt;&lt;font size=2&gt;i&lt;/font&gt;&lt;/sub&gt; &lt;br&gt;
        fim para &lt;br&gt;
        retorna p </traducao>
    <traducao xml:lang="en-us"/>
  </sentenca>
  <sentenca xml:id="LAGRANGE_AJUDA">
    <traducao xml:lang="pt-br">
        &lt;ul&gt;
        &lt;li&gt;Os arquivos devem estar no formato .txt, e os valores escritos em formato texto.&lt;/li&gt; &lt;br&gt; &lt;br&gt;
        &lt;li&gt;Cada linha deve conter apenas &lt;b&gt;um&lt;/b&gt; valor, na seguinte ordem: &lt;/li&gt; &lt;br&gt; &lt;br&gt;
        &lt;li&gt; &lt;b&gt; Arquivo de dados &lt;/b&gt;
        &lt;br&gt;
        &lt;br&gt; 1ª linha: '0' (Zero) para caso discreto (entrada de dados através de um conjunto de pontos) ou '1' para caso contínuo (entrada de dados através de uma função e um intervalo). &lt;br&gt;
        &lt;br&gt; 2ª linha: Para o caso discreto, '0' (Zero). Para o caso contínuo, '1' se a distribuição dos pontos uniforme ou '2' se a distribuição for de Chebyshev. &lt;br&gt; 
        &lt;br&gt; 3ª linha: número de pontos. &lt;br&gt; 
        &lt;br&gt; Para o caso discreto:
        &lt;ul&gt;
        &lt;li&gt;  &lt;br&gt; A partir da 4ª linha: digitar valores dos pares de pontos x e y, um par em cada linha, da seguinte maneira: x&lt;font size=4&gt;&lt;b&gt;;&lt;/b&gt;&lt;/font&gt;y. &lt;br&gt; &lt;/li&gt;
        &lt;/ul&gt;    
        &lt;br&gt; Para o caso contínuo:
        &lt;ul&gt;
        &lt;li&gt; &lt;br&gt; 4ª linha: função do problema, no &lt;a href=javascript:winopen('funcoesphp.php')&gt;formato&lt;/a&gt; reconhecido pelo programa. &lt;br&gt; &lt;/li&gt;
        &lt;li&gt; &lt;br&gt; 5ª linha: intervalo a,b da função, escrito na forma: a&lt;font size=4&gt;&lt;b&gt;;&lt;/b&gt;&lt;/font&gt;b. &lt;br&gt; &lt;/li&gt;
        &lt;/ul&gt;    
        &lt;br&gt; 
        &lt;br&gt; Última linha: valor a ser interpolado. &lt;br&gt; &lt;br&gt;
        &lt;li&gt; &lt;b&gt; Arquivo de resposta &lt;/b&gt;
        &lt;br&gt;
        &lt;br&gt; 1ª linha: valor interpolado. &lt;br&gt;
        &lt;/ul&gt;
    </traducao>
    <traducao xml:lang="en-us"/>
  </sentenca>
  <sentenca xml:id="LUDECOMP_MSG_01">
    <traducao xml:lang="pt-br">Decomposição LU</traducao>
    <traducao xml:lang="en-us">LU Decomposition</traducao>
  </sentenca>
  <sentenca xml:id="LUDECOMP_MSG_02">
    <traducao xml:lang="pt-br">Sistemas de Equações Algébricas Lineares</traducao>
    <traducao xml:lang="en-us">System of Linear Algebraic Equation</traducao>
  </sentenca>
  <sentenca xml:id="LUDECOMP_MSG_03">
    <traducao xml:lang="pt-br">Decomposição LU</traducao>
    <traducao xml:lang="en-us">LU Decomposition</traducao>
  </sentenca>
  <sentenca xml:id="LUDECOMP_MSG_04">
    <traducao xml:lang="pt-br">Dimensão (número de variáveis): </traducao>
    <traducao xml:lang="en-us">Dimension (number of variables): </traducao>
  </sentenca>
  <sentenca xml:id="LUDECOMP_MSG_05">
    <traducao xml:lang="pt-br">Sistema</traducao>
    <traducao xml:lang="en-us">System</traducao>
  </sentenca>
  <sentenca xml:id="LUDECOMP_MSG_06">
    <traducao xml:lang="pt-br">Solução retirada do arquivo: </traducao>
    <traducao xml:lang="en-us">Extracted solution of the arquive </traducao>
  </sentenca>
  <sentenca xml:id="LUDECOMP_MSG_07">
    <traducao xml:lang="pt-br">Matriz A</traducao>
    <traducao xml:lang="en-us">Matrix A</traducao>
  </sentenca>
  <sentenca xml:id="LUDECOMP_MSG_08">
    <traducao xml:lang="pt-br">Matriz L</traducao>
    <traducao xml:lang="en-us">Matrix L</traducao>
  </sentenca>
  <sentenca xml:id="LUDECOMP_MSG_09">
    <traducao xml:lang="pt-br">Matriz U</traducao>
    <traducao xml:lang="en-us">Matrix U</traducao>
  </sentenca>
  <sentenca xml:id="LUDECOMP_MSG_10">
    <traducao xml:lang="pt-br">Não foi possível executar o método pois o determinante da matriz é zero!</traducao>
    <traducao xml:lang="en-us">It was not possible to execute the method because the determinant of the matrix is null!</traducao>
  </sentenca>
  <sentenca xml:id="LUDECOMP_MSG_11">
    <traducao xml:lang="pt-br">Solução obtida do programa: </traducao>
    <traducao xml:lang="en-us">Gotten solution of the program: </traducao>
  </sentenca>
  <sentenca xml:id="LUDECOMP_MSG_12">
    <traducao xml:lang="pt-br">Solução obtida do arquivo: </traducao>
    <traducao xml:lang="en-us">Gotten solution of the archive: </traducao>
  </sentenca>
  <sentenca xml:id="LUDECOMP_MSG_13">
    <traducao xml:lang="pt-br">Não é possível executar o método, pois o determinante de uma das submatrizes é zero</traducao>
    <traducao xml:lang="en-us">It is not possible to execute the method, because the determinant of one of the submatrices is null</traducao>
  </sentenca>
  <sentenca xml:id="LUDECOMP_ALGORITMO">
    <traducao xml:lang="pt-br">
        &lt;b&gt;Variáveis: &lt;/b&gt; &lt;br&gt;&lt;br&gt; 
        Auxiliares: &lt;br&gt;
        h, i, j, k, p (contadores), L, U, Uy, Lt (matrizes), VetY (vetor), soma&lt;br&gt;&lt;br&gt;
        De entrada: &lt;br&gt;
        dim (dimensão da matriz), A e T (matriz e vetor, para o sistema A x = T)  &lt;br&gt;&lt;br&gt;
        De saída: &lt;br&gt;
        VetX (vetor - quando há solução)&lt;br&gt;&lt;br&gt;
        &lt;b&gt;Algoritmo: &lt;/b&gt; &lt;br&gt;&lt;br&gt; 
        função retrosubstituição(B,dim) &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; VetX&lt;sub&gt;&lt;font size=2&gt;dim-1&lt;/font&gt;&lt;/sub&gt; := B&lt;sub&gt;&lt;font size=2&gt;dim-1,dim&lt;/font&gt;&lt;/sub&gt;/B&lt;sub&gt;&lt;font size=2&gt;dim-1,dim-1&lt;/font&gt;&lt;/sub&gt; &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; para k de dim-2 a 0 faça &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; VetX&lt;sub&gt;&lt;font size=2&gt;k&lt;/font&gt;&lt;/sub&gt; := B&lt;sub&gt;&lt;font size=2&gt;k,dim&lt;/font&gt;&lt;/sub&gt; &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; para i de k+1 a dim-1 faça &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; VetX&lt;sub&gt;&lt;font size=2&gt;k&lt;/font&gt;&lt;/sub&gt; := VetX&lt;sub&gt;&lt;font size=2&gt;k&lt;/font&gt;&lt;/sub&gt; - B&lt;sub&gt;&lt;font size=2&gt;k,i&lt;/font&gt;&lt;/sub&gt; * VetX&lt;sub&gt;&lt;font size=2&gt;i&lt;/font&gt;&lt;/sub&gt; &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim para &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; VetX&lt;sub&gt;&lt;font size=2&gt;k&lt;/font&gt;&lt;/sub&gt; := VetX&lt;sub&gt;&lt;font size=2&gt;k&lt;/font&gt;&lt;/sub&gt; / B&lt;sub&gt;&lt;font size=2&gt;k,k&lt;/font&gt;&lt;/sub&gt; &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim para &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; retorna VetX &lt;br&gt;
        fim função &lt;br&gt; &lt;br&gt;
        funçao forwardsubstituição(f,dim)  &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; VetY&lt;sub&gt;&lt;font size=2&gt;0&lt;/font&gt;&lt;/sub&gt; := f&lt;sub&gt;&lt;font size=2&gt;0,dim&lt;/font&gt;&lt;/sub&gt;/f&lt;sub&gt;&lt;font size=2&gt;0,0&lt;/font&gt;&lt;/sub&gt; &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; para i de 1 a dim-1 faça &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; soma := 0 &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; para j de 0 a i-1 faça &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; soma = soma + f&lt;sub&gt;&lt;font size=2&gt;i,j&lt;/font&gt;&lt;/sub&gt;*VetY&lt;sub&gt;&lt;font size=2&gt;j&lt;/font&gt;&lt;/sub&gt; &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim para &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; VetY&lt;sub&gt;&lt;font size=2&gt;i&lt;/font&gt;&lt;/sub&gt; := (f&lt;sub&gt;&lt;font size=2&gt;i,dim&lt;/font&gt;&lt;/sub&gt;-soma)/f&lt;sub&gt;&lt;font size=2&gt;i,i&lt;/font&gt;&lt;/sub&gt; &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim para &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; retorna VetY &lt;br&gt;
        fim função &lt;br&gt; &lt;br&gt;
        função somatório(B,C,l1,c2,ini,fim) &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; soma := 0 &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; para p de ini a fim faça &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; soma = B&lt;sub&gt;&lt;font size=2&gt;l1,p&lt;/font&gt;&lt;/sub&gt;*C&lt;sub&gt;&lt;font size=2&gt;p,c2&lt;/font&gt;&lt;/sub&gt; &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim para &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; retorna soma &lt;br&gt;
        fim função &lt;br&gt; &lt;br&gt;
        se determinante(A) diferente de zero então &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; para i de 0 a dim-1 faça &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; para j de 0 a dim-1 faça &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; se i&lt;j então &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; U&lt;sub&gt;&lt;font size=2&gt;i,j&lt;/font&gt;&lt;/sub&gt; := A&lt;sub&gt;&lt;font size=2&gt;i,j&lt;/font&gt;&lt;/sub&gt;-somatório(L,U,i,j,0,i-1) &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim se &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; senão &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; se i = j então &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; U&lt;sub&gt;&lt;font size=2&gt;i,j&lt;/font&gt;&lt;/sub&gt; := A&lt;sub&gt;&lt;font size=2&gt;i,j&lt;/font&gt;&lt;/sub&gt;-somatório(L,U,i,j,0,i-1) &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; L&lt;sub&gt;&lt;font size=2&gt;i,j&lt;/font&gt;&lt;/sub&gt; := (A&lt;sub&gt;&lt;font size=2&gt;i,j&lt;/font&gt;&lt;/sub&gt;-somatório(L,U,i,j,0,j-1))/U&lt;sub&gt;&lt;font size=2&gt;j,j&lt;/font&gt;&lt;/sub&gt; &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim se &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; senão &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; L&lt;sub&gt;&lt;font size=2&gt;i,j&lt;/font&gt;&lt;/sub&gt; := (A&lt;sub&gt;&lt;font size=2&gt;i,j&lt;/font&gt;&lt;/sub&gt;-somatório(L,U,i,j,0,j-1))/U&lt;sub&gt;&lt;font size=2&gt;j,j&lt;/font&gt;&lt;/sub&gt; &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim senão &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim senão &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim para &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim para &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; para h de 0 a dim-1 faça &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; para p de 0 a dim faça &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; se p=dim então &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; Lt&lt;sub&gt;&lt;font size=2&gt;h,p&lt;/font&gt;&lt;/sub&gt; := T&lt;sub&gt;&lt;font size=2&gt;h&lt;/font&gt;&lt;/sub&gt; &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim se &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; senão &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; Lt&lt;sub&gt;&lt;font size=2&gt;h,p&lt;/font&gt;&lt;/sub&gt; := L&lt;sub&gt;&lt;font size=2&gt;h,p&lt;/font&gt;&lt;/sub&gt; &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim senão &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim para &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim para &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; VetY := forwardsubstituição(Lt,dim) &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; para h de 0 a dim-1 faça &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; para p de 0 a dim faça &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; se p = dim então &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; Uy&lt;sub&gt;&lt;font size=2&gt;h,p&lt;/font&gt;&lt;/sub&gt; := VetY&lt;sub&gt;&lt;font size=2&gt;h&lt;/font&gt;&lt;/sub&gt; &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim se &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; senão &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; Uy&lt;sub&gt;&lt;font size=2&gt;h,p&lt;/font&gt;&lt;/sub&gt; := U&lt;sub&gt;&lt;font size=2&gt;h,p&lt;/font&gt;&lt;/sub&gt; &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim senão &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim para &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim para &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; VetX := retrosubstituição(Uy,dim) &lt;br&gt;     
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; retorna VetX &lt;br&gt;
        fim se &lt;br&gt;
        senão 'O problema não possui solução pois a matriz não possui determinante' &lt;br&gt;</traducao>
    <traducao xml:lang="en-us"/>
  </sentenca>
  <sentenca xml:id="LUDECOMP_AJUDA">
    <traducao xml:lang="pt-br">
        &lt;ul&gt;
        &lt;li&gt;Os arquivos devem estar no formato .txt.&lt;/li&gt; &lt;br&gt;
        &lt;li&gt;Cada linha deve conter apenas &lt;b&gt;um&lt;/b&gt; valor, na seguinte ordem: &lt;/li&gt; &lt;br&gt;
        &lt;li&gt; &lt;b&gt; Arquivo de dados &lt;/b&gt;
        &lt;br&gt;
        &lt;br&gt; 1ª linha: dimensão da matriz A. &lt;br&gt;
        &lt;br&gt; A partir da 2ª linha: elementos da matriz A, a partir da primeira linha. Ao final de cada linha, inserir o valor da matriz B, tal que A x = B. &lt;br&gt;
        &lt;br&gt;
        &lt;li&gt; &lt;b&gt; Arquivo de resposta &lt;/b&gt;
        &lt;br&gt;
        &lt;br&gt; A partir da 1ª linha: elementos do vetor resposta. &lt;br&gt;
        &lt;/ul&gt;
    </traducao>
    <traducao xml:lang="en-us"/>
  </sentenca>
  <sentenca xml:id="MATDEFPOS_MSG_01">
    <traducao xml:lang="pt-br">Matrizes definidas positivas - Verificação</traducao>
    <traducao xml:lang="en-us">Positive definite matrices</traducao>
  </sentenca>
  <sentenca xml:id="MATDEFPOS_MSG_02">
    <traducao xml:lang="pt-br">Aritmética Matricial</traducao>
    <traducao xml:lang="en-us">Matricial Arithmetic</traducao>
  </sentenca>
  <sentenca xml:id="MATDEFPOS_MSG_03">
    <traducao xml:lang="pt-br">Matrizes definidas positivas</traducao>
    <traducao xml:lang="en-us">Positive definite matrices</traducao>
  </sentenca>
  <sentenca xml:id="MATDEFPOS_MSG_04">
    <traducao xml:lang="pt-br">Dimensão: </traducao>
    <traducao xml:lang="en-us">Dimension: </traducao>
  </sentenca>
  <sentenca xml:id="MATDEFPOS_MSG_05">
    <traducao xml:lang="pt-br">Matriz A</traducao>
    <traducao xml:lang="en-us">Matrix A</traducao>
  </sentenca>
  <sentenca xml:id="MATDEFPOS_MSG_06">
    <traducao xml:lang="pt-br">Resposta obtida do arquivo:</traducao>
    <traducao xml:lang="en-us">Gotten answer of the archive:</traducao>
  </sentenca>
  <sentenca xml:id="MATDEFPOS_MSG_07">
    <traducao xml:lang="pt-br">Resposta obtida do programa: </traducao>
    <traducao xml:lang="en-us">Gotten answer of the program: </traducao>
  </sentenca>
  <sentenca xml:id="MATDEFPOS_MSG_08">
    <traducao xml:lang="pt-br">Determinantes das submatrizes: </traducao>
    <traducao xml:lang="en-us">Determinants of the submatrices: </traducao>
  </sentenca>
  <sentenca xml:id="MATDEFPOS_MSG_09">
    <traducao xml:lang="pt-br">A matriz é definida positiva, pois o determinante de todas as submatrizes são maiores que 0.</traducao>
    <traducao xml:lang="en-us">The matrix is positive definite.</traducao>
  </sentenca>
  <sentenca xml:id="MATDEFPOS_MSG_10">
    <traducao xml:lang="pt-br">A matriz não é definida positiva.</traducao>
    <traducao xml:lang="en-us">The matrix isn't positive definite.</traducao>
  </sentenca>
  <sentenca xml:id="MATDEFPOS_MSG_11">
    <traducao xml:lang="pt-br">Submatriz </traducao>
    <traducao xml:lang="en-us">Submatrix</traducao>
  </sentenca>
  <sentenca xml:id="MATDEFPOS_MSG_12">
    <traducao xml:lang="pt-br">Determinante da submatriz </traducao>
    <traducao xml:lang="en-us">Determinant of the submatrix </traducao>
  </sentenca>
  <sentenca xml:id="MATDEFPOS_MSG_13">
    <traducao xml:lang="pt-br">A matriz não é simétrica.</traducao>
    <traducao xml:lang="en-us">The matrix is not symetric</traducao>
  </sentenca>
  <sentenca xml:id="MATDEFPOS_MSG_14">
    <traducao xml:lang="pt-br">Matriz</traducao>
    <traducao xml:lang="en-us">Matrix</traducao>
  </sentenca>
  <sentenca xml:id="MATDEFPOS_MSG_15">
    <traducao xml:lang="pt-br">A matriz é simétrica.</traducao>
    <traducao xml:lang="en-us">The matrix is symetric</traducao>
  </sentenca>
  <sentenca xml:id="MATDEFPOS_ALGORITMO">
    <traducao xml:lang="pt-br">
        &lt;b&gt;Variáveis: &lt;/b&gt; &lt;br&gt;&lt;br&gt; 
        Auxiliares: &lt;br&gt;
        i, j (contadores), vetor, positiva (booleano) &lt;br&gt;&lt;br&gt;
        De entrada: &lt;br&gt;
        A (matriz), dim (dimensão da matriz) &lt;br&gt;&lt;br&gt;
        De saída: &lt;br&gt;
        booleano (positivo ou negativo) &lt;br&gt;&lt;br&gt;
        &lt;b&gt;Algoritmo: &lt;/b&gt; &lt;br&gt;&lt;br&gt; 
        positiva := sim &lt;br&gt;
        para i de 0 a dim-1 faça &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; vetor&lt;sub&gt;&lt;font size=2&gt;i&lt;/font&gt;&lt;/sub&gt; := determinante (A&lt;sub&gt;&lt;font size=2&gt;i,i&lt;/font&gt;&lt;/sub&gt;) , onde A&lt;sub&gt;&lt;font size=2&gt;i,i&lt;/font&gt;&lt;/sub&gt; é a submatriz de A, de dimensão i &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; se vetor&lt;sub&gt;&lt;font size=2&gt;i&lt;/font&gt;&lt;/sub&gt; &lt;= 0 então &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; positiva := nao &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim se &lt;br&gt;  
        fim para i &lt;br&gt;
        se positiva = nao então &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; retorna 'A matriz não é definida positiva' &lt;br&gt;
        fim se &lt;br&gt;
        senão &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; retorna 'A matriz é definida positiva' &lt;br&gt;
        fim senão </traducao>
    <traducao xml:lang="en-us"/>
  </sentenca>
  <sentenca xml:id="MATDEFPOS_AJUDA">
    <traducao xml:lang="pt-br">
        &lt;ul&gt;
        &lt;li&gt;Os arquivos devem estar no formato .txt.&lt;/li&gt; &lt;br&gt;
        &lt;li&gt;Cada linha deve conter apenas &lt;b&gt;um&lt;/b&gt; valor, na seguinte ordem: &lt;/li&gt; &lt;br&gt;
        &lt;li&gt; &lt;b&gt; Arquivo de dados &lt;/b&gt;
        &lt;br&gt;
        &lt;br&gt; 1ª linha: dimensão da matriz A. &lt;br&gt;
        &lt;br&gt; A partir da 2ª linha: elementos da matriz A, em ordem crescente de coluna e linha. &lt;br&gt;
        &lt;br&gt;
        &lt;li&gt; &lt;b&gt; Arquivo de resposta &lt;/b&gt;
        &lt;br&gt;
        &lt;br&gt; 1ª linha: determinante da submatriz 1 x 1. &lt;br&gt;
        &lt;br&gt; 2ª linha: determinante da submatriz 2 x 2. &lt;br&gt;   
        &lt;br&gt; nª linha: determinante da submatriz n x n. &lt;br&gt; 
        &lt;br&gt; Última linha: 
        &lt;br&gt; 1 - caso a matriz seja definida positiva
        &lt;br&gt; 0 - caso a matriz não seja definida positiva
        &lt;/ul&gt;      </traducao>
    <traducao xml:lang="en-us"/>
  </sentenca>
  <sentenca xml:id="MULTIPLICACAO_MSG_01">
    <traducao xml:lang="pt-br">Multiplicação de Matrizes</traducao>
    <traducao xml:lang="en-us">Multiplication of Matrices</traducao>
  </sentenca>
  <sentenca xml:id="MULTIPLICACAO_MSG_02">
    <traducao xml:lang="pt-br">Aritmética Matricial</traducao>
    <traducao xml:lang="en-us">Matricial Arithmetic</traducao>
  </sentenca>
  <sentenca xml:id="MULTIPLICACAO_MSG_03">
    <traducao xml:lang="pt-br">Multiplicação</traducao>
    <traducao xml:lang="en-us">Multiplication</traducao>
  </sentenca>
  <sentenca xml:id="MULTIPLICACAO_MSG_04">
    <traducao xml:lang="pt-br">Dimensão da matriz A: </traducao>
    <traducao xml:lang="en-us">Dimension of matrix A: </traducao>
  </sentenca>
  <sentenca xml:id="MULTIPLICACAO_MSG_09">
    <traducao xml:lang="pt-br">Dimensão da matriz B: </traducao>
    <traducao xml:lang="en-us">Dimension of matrix B: </traducao>
  </sentenca>
  <sentenca xml:id="MULTIPLICACAO_MSG_05">
    <traducao xml:lang="pt-br">Matriz A</traducao>
    <traducao xml:lang="en-us">Matrix A</traducao>
  </sentenca>
  <sentenca xml:id="MULTIPLICACAO_MSG_06">
    <traducao xml:lang="pt-br">Matriz B</traducao>
    <traducao xml:lang="en-us">Matrix B</traducao>
  </sentenca>
  <sentenca xml:id="MULTIPLICACAO_MSG_07">
    <traducao xml:lang="pt-br">Matriz C (A x B)&lt;br&gt;Resposta retirada do arquivo:</traducao>
    <traducao xml:lang="en-us">Matrix C (A x B) - Extracted answer of the archive:</traducao>
  </sentenca>
  <sentenca xml:id="MULTIPLICACAO_MSG_08">
    <traducao xml:lang="pt-br">Matriz C (A x B)&lt;br&gt;Resposta obtida do programa: </traducao>
    <traducao xml:lang="en-us">Matrix C (A x B) - Gotten answer of the program: </traducao>
  </sentenca>
  <sentenca xml:id="MULTIPLICACAO_MSG_10">
    <traducao xml:lang="pt-br">Dimensão inválida. Insira uma dimensão válida para as matrizes.</traducao>
    <traducao xml:lang="en-us">Invalid dimension. Type a valid dimension for the matrices.</traducao>
  </sentenca>
  <sentenca xml:id="MULTIPLICACAO_ALGORITMO">
    <traducao xml:lang="pt-br">
        &lt;b&gt;Variáveis: &lt;/b&gt; &lt;br&gt;&lt;br&gt; 
        Auxiliares: &lt;br&gt;
        i, j, k (contadores) &lt;br&gt;&lt;br&gt;
        De entrada: &lt;br&gt;
        A e B (matrizes de dimensão rows1 x cols1 e rows2 x cols2, onde cols1 = rows2), rows1, cols1, rows2, cols2 &lt;br&gt;&lt;br&gt;
        De saída: &lt;br&gt;
        C (matriz de dimensão rows1 x cols2)&lt;br&gt;&lt;br&gt;
        &lt;b&gt;Algoritmo: &lt;/b&gt; &lt;br&gt;&lt;br&gt; 
        para i de 0 a rows1-1 faça &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; para j de 0 a cols2-1 faça &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; C&lt;sub&gt;&lt;font size=2&gt;i,j&lt;/font&gt;&lt;/sub&gt; := 0 &lt;br&gt;    
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; para k de 0 a cols1-1 faça &lt;br&gt;  
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; C&lt;sub&gt;&lt;font size=2&gt;i,j&lt;/font&gt;&lt;/sub&gt; := C&lt;sub&gt;&lt;font size=2&gt;i,j&lt;/font&gt;&lt;/sub&gt; + A&lt;sub&gt;&lt;font size=2&gt;i,k&lt;/font&gt;&lt;/sub&gt;*B&lt;sub&gt;&lt;font size=2&gt;k,j&lt;/font&gt;&lt;/sub&gt; &lt;br&gt;        
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim para k &lt;br&gt;  
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim para j &lt;br&gt;
        fim para i &lt;br&gt;
        retorna C </traducao>
    <traducao xml:lang="en-us"/>
  </sentenca>
  <sentenca xml:id="MULTIPLICACAO_AJUDA">
    <traducao xml:lang="pt-br">
        &lt;ul&gt;
        &lt;li&gt;Os arquivos devem estar no formato .txt.&lt;/li&gt; &lt;br&gt;
        &lt;li&gt;Cada linha deve conter apenas &lt;b&gt;um&lt;/b&gt; valor, na seguinte ordem: &lt;/li&gt; &lt;br&gt; 
        &lt;li&gt; &lt;b&gt; Arquivo de dados &lt;/b&gt;
        &lt;br&gt;
        &lt;br&gt; 1ª linha: número de linhas da matriz A. &lt;br&gt;
        &lt;br&gt; 2ª linha: número de colunas da matriz A. &lt;br&gt;
        &lt;br&gt; 3ª linha: número de linhas da matriz B. &lt;br&gt;
        &lt;br&gt; 4ª linha: número de colunas da matriz B. &lt;br&gt;
        &lt;br&gt; A partir da 4ª linha: elementos da matriz A, em ordem crescente de coluna e linha. &lt;br&gt;
        &lt;br&gt; Em seguida: elementos da matriz B, em ordem crescente de coluna e linha. &lt;br&gt;
        &lt;br&gt;
        &lt;li&gt; &lt;b&gt; Arquivo de resposta &lt;/b&gt;
        &lt;br&gt;
        &lt;br&gt; A partir da 1ª linha: elementos da matriz C, em ordem crescente de coluna e linha. &lt;br&gt;
        &lt;/ul&gt;
    </traducao>
    <traducao xml:lang="en-us"/>
  </sentenca>
  <sentenca xml:id="NEWTON_MSG_01">
    <traducao xml:lang="pt-br">Método de Newton - Diferenças Divididas</traducao>
    <traducao xml:lang="en-us">Newton Method - Divided Differences</traducao>
  </sentenca>
  <sentenca xml:id="NEWTON_MSG_02">
    <traducao xml:lang="pt-br">Interpolação Polinomial</traducao>
    <traducao xml:lang="en-us">Polynomial Interpolation</traducao>
  </sentenca>
  <sentenca xml:id="NEWTON_MSG_03">
    <traducao xml:lang="pt-br">Diferenças divididas</traducao>
    <traducao xml:lang="en-us">Divided differences</traducao>
  </sentenca>
  <sentenca xml:id="NEWTON_MSG_04">
    <traducao xml:lang="pt-br">Selecione uma opção para entrada de dados:</traducao>
    <traducao xml:lang="en-us">Select an option of problem:</traducao>
  </sentenca>
  <sentenca xml:id="NEWTON_MSG_05">
    <traducao xml:lang="pt-br">Caso discreto (através de um conjunto de pontos)</traducao>
    <traducao xml:lang="en-us">Discrete case (through a set of points)</traducao>
  </sentenca>
  <sentenca xml:id="NEWTON_MSG_06">
    <traducao xml:lang="pt-br">Caso contínuo (através de uma função e um intervalo)</traducao>
    <traducao xml:lang="en-us">Continuous case (through a function and a interval)</traducao>
  </sentenca>
  <sentenca xml:id="NEWTON_MSG_07">
    <traducao xml:lang="pt-br">Digite o número de pontos que serão dados como entrada:</traducao>
    <traducao xml:lang="en-us">Type the number of points that will be given as entry:</traducao>
  </sentenca>
  <sentenca xml:id="NEWTON_MSG_09">
    <traducao xml:lang="pt-br">Digite a função: </traducao>
    <traducao xml:lang="en-us">Type the function: </traducao>
  </sentenca>
  <sentenca xml:id="NEWTON_MSG_10">
    <traducao xml:lang="pt-br">Digite o intervalo em que a função será aproximada: </traducao>
    <traducao xml:lang="en-us">Type the interval where the function will be aproached: </traducao>
  </sentenca>
  <sentenca xml:id="NEWTON_MSG_11">
    <traducao xml:lang="pt-br">Tipo de distribuição dos </traducao>
    <traducao xml:lang="en-us">Type of distribution of the </traducao>
  </sentenca>
  <sentenca xml:id="NEWTON_MSG_12">
    <traducao xml:lang="pt-br"> pontos no intervalo </traducao>
    <traducao xml:lang="en-us"> points of the interval </traducao>
  </sentenca>
  <sentenca xml:id="NEWTON_MSG_13">
    <traducao xml:lang="pt-br">Distribuição uniforme</traducao>
    <traducao xml:lang="en-us">Uniform distribution</traducao>
  </sentenca>
  <sentenca xml:id="NEWTON_MSG_14">
    <traducao xml:lang="pt-br">Distribuição de Chebyshev</traducao>
    <traducao xml:lang="en-us">Chebyshev distribution</traducao>
  </sentenca>
  <sentenca xml:id="NEWTON_MSG_15">
    <traducao xml:lang="pt-br">Número de pontos:</traducao>
    <traducao xml:lang="en-us">Number of points:</traducao>
  </sentenca>
  <sentenca xml:id="NEWTON_MSG_16">
    <traducao xml:lang="pt-br">Grau do polinômio p(x): </traducao>
    <traducao xml:lang="en-us">Degree of the polynomial p(x) </traducao>
  </sentenca>
  <sentenca xml:id="NEWTON_MSG_17">
    <traducao xml:lang="pt-br">Função dada:</traducao>
    <traducao xml:lang="en-us">Given function:</traducao>
  </sentenca>
  <sentenca xml:id="NEWTON_MSG_18">
    <traducao xml:lang="pt-br">Intervalo </traducao>
    <traducao xml:lang="en-us">Intervalo </traducao>
  </sentenca>
  <sentenca xml:id="NEWTON_MSG_19">
    <traducao xml:lang="pt-br">Valores de (x , y):</traducao>
    <traducao xml:lang="en-us">Values of (x,y):</traducao>
  </sentenca>
  <sentenca xml:id="NEWTON_MSG_20">
    <traducao xml:lang="pt-br">Calcular p(x) para x= </traducao>
    <traducao xml:lang="en-us">Calculate p(x) where x= </traducao>
  </sentenca>
  <sentenca xml:id="NEWTON_MSG_21">
    <traducao xml:lang="pt-br">Resposta retirada do arquivo: </traducao>
    <traducao xml:lang="en-us">Extracted answer of the archive: </traducao>
  </sentenca>
  <sentenca xml:id="NEWTON_MSG_22">
    <traducao xml:lang="pt-br">Resposta obtida do programa: </traducao>
    <traducao xml:lang="en-us">Gotten answer of the program: </traducao>
  </sentenca>
  <sentenca xml:id="NEWTON_MSG_23">
    <traducao xml:lang="pt-br">Resposta obtida do arquivo: </traducao>
    <traducao xml:lang="en-us">Gotten answer of the archive: </traducao>
  </sentenca>
  <sentenca xml:id="NEWTON_MSG_24">
    <traducao xml:lang="pt-br">Tabela de Diferenças Divididas</traducao>
    <traducao xml:lang="en-us">Table of Divided Differences</traducao>
  </sentenca>
  <sentenca xml:id="NEWTON_MSG_25">
    <traducao xml:lang="pt-br">Diferenças divididas de ordem </traducao>
    <traducao xml:lang="en-us">Divided Differences of order </traducao>
  </sentenca>
  <sentenca xml:id="NEWTON_MSG_26">
    <traducao xml:lang="pt-br">Polinômio interpolador:</traducao>
    <traducao xml:lang="en-us">Polynomial interpolater:</traducao>
  </sentenca>
  <sentenca xml:id="NEWTON_MSG_27">
    <traducao xml:lang="pt-br">Para x= </traducao>
    <traducao xml:lang="en-us">Where x= </traducao>
  </sentenca>
  <sentenca xml:id="NEWTON_MSG_28">
    <traducao xml:lang="pt-br">Valor acumulado</traducao>
    <traducao xml:lang="en-us"> we have: </traducao>
  </sentenca>
  <sentenca xml:id="NEWTON_MSG_29">
    <traducao xml:lang="pt-br">&amp;nbsp;</traducao>
    <traducao xml:lang="en-us">Accumulated value</traducao>
  </sentenca>
  <sentenca xml:id="NEWTON_ALGORITMO">
    <traducao xml:lang="pt-br">
        &lt;b&gt;Variáveis: &lt;/b&gt; &lt;br&gt;&lt;br&gt; 
        Auxiliares: &lt;br&gt;
        i, k (contadores), tabela (matriz), l &lt;br&gt;&lt;br&gt;
        De entrada: &lt;br&gt;
        n (número de pontos), X e Y (vetores), valor (ponto a ser interpolado)  &lt;br&gt;&lt;br&gt;
        De saída: &lt;br&gt;
        p (resultado da interpolação no ponto 'valor')&lt;br&gt;&lt;br&gt;
        &lt;b&gt;Algoritmo: &lt;/b&gt; &lt;br&gt;&lt;br&gt; 
        // construção da tabela de diferenças divididas &lt;br&gt;
        para i de 0 a n-1 faça &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; tabela&lt;sub&gt;&lt;font size=2&gt;i,-1&lt;/font&gt;&lt;/sub&gt; := X&lt;sub&gt;&lt;font size=2&gt;i&lt;/font&gt;&lt;/sub&gt; &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; tabela&lt;sub&gt;&lt;font size=2&gt;i,0&lt;/font&gt;&lt;/sub&gt; := Y&lt;sub&gt;&lt;font size=2&gt;i&lt;/font&gt;&lt;/sub&gt; &lt;br&gt;
        fim para &lt;br&gt;
        para k de 1 a n-1 faça &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; para i de k a n-1 faça &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; tabela&lt;sub&gt;&lt;font size=2&gt;i,k&lt;/font&gt;&lt;/sub&gt; := (tabela&lt;sub&gt;&lt;font size=2&gt;i,k-1&lt;/font&gt;&lt;/sub&gt; - tabela&lt;sub&gt;&lt;font size=2&gt;i-1,k-1&lt;/font&gt;&lt;/sub&gt;) / (tabela&lt;sub&gt;&lt;font size=2&gt;i,-1&lt;/font&gt;&lt;/sub&gt; - tabela&lt;sub&gt;&lt;font size=2&gt;i-k,-1&lt;/font&gt;&lt;/sub&gt;) &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim para &lt;br&gt;
        fim para &lt;br&gt;
        // interpolação  &lt;br&gt;
        p := 0 &lt;br&gt;
        para i de 0 a n-1 faça &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; l := 1  &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; para t de i a 1 faça &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; l := l * valor - X&lt;sub&gt;&lt;font size=2&gt;t-1&lt;/font&gt;&lt;/sub&gt; &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim para &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; p := p + tabela&lt;sub&gt;&lt;font size=2&gt;i,i&lt;/font&gt;&lt;/sub&gt; * l &lt;br&gt;
        fim para &lt;br&gt;
        retorna p  </traducao>
    <traducao xml:lang="en-us"/>
  </sentenca>
  <sentenca xml:id="NEWTON_AJUDA">
    <traducao xml:lang="pt-br">
        &lt;ul&gt;
        &lt;li&gt;Os arquivos devem estar no formato .txt, e os valores escritos em formato texto.&lt;/li&gt; &lt;br&gt; &lt;br&gt;
        &lt;li&gt;Cada linha deve conter apenas &lt;b&gt;um&lt;/b&gt; valor, na seguinte ordem: &lt;/li&gt; &lt;br&gt; &lt;br&gt;
        &lt;li&gt; &lt;b&gt; Arquivo de dados &lt;/b&gt;
        &lt;br&gt;
        &lt;br&gt; 1ª linha: '0' (Zero) para caso discreto (entrada de dados através de um conjunto de pontos) ou '1' para caso contínuo (entrada de dados através de uma função e um intervalo). &lt;br&gt;
        &lt;br&gt; 2ª linha: Para o caso discreto, '0' (Zero). Para o caso contínuo, '1' se a distribuição dos pontos uniforme ou '2' se a distribuição for de Chebyshev. &lt;br&gt; 
        &lt;br&gt; 3ª linha: número de pontos. &lt;br&gt; 
        &lt;br&gt; Para o caso discreto:
        &lt;ul&gt;
        &lt;li&gt;  &lt;br&gt; A partir da 4ª linha: digitar valores dos pares de pontos x e y, um par em cada linha, da seguinte maneira: x&lt;font size=4&gt;&lt;b&gt;;&lt;/b&gt;&lt;/font&gt;y. &lt;br&gt; &lt;/li&gt;
        &lt;/ul&gt;    
        &lt;br&gt; Para o caso contínuo:
        &lt;ul&gt;
        &lt;li&gt; &lt;br&gt; 4ª linha: função do problema, no &lt;a href=javascript:winopen('funcoesphp.php')&gt;formato&lt;/a&gt; reconhecido pelo programa. &lt;br&gt; &lt;/li&gt;
        &lt;li&gt; &lt;br&gt; 5ª linha: intervalo a,b da função, escrito na forma: a&lt;font size=4&gt;&lt;b&gt;;&lt;/b&gt;&lt;/font&gt;b. &lt;br&gt; &lt;/li&gt;
        &lt;/ul&gt;    
        &lt;br&gt; 
        &lt;br&gt; Última linha: valor a ser interpolado. &lt;br&gt; &lt;br&gt;
        &lt;li&gt; &lt;b&gt; Arquivo de resposta &lt;/b&gt;
        &lt;br&gt;
        &lt;br&gt; 1ª linha: valor interpolado. &lt;br&gt;
        &lt;/ul&gt;
    </traducao>
    <traducao xml:lang="en-us"/>
  </sentenca>
  <sentenca xml:id="SEQNL_MSG_01">
    <traducao xml:lang="pt-br">Método de Newton</traducao>
    <traducao xml:lang="en-us">Newton Method</traducao>
  </sentenca>
  <sentenca xml:id="SEQNL_MSG_02">
    <traducao xml:lang="pt-br">Sistemas de Equações Algébricas Não-Lineares</traducao>
    <traducao xml:lang="en-us">Systems of Nonlinear Algebraic Equations</traducao>
  </sentenca>
  <sentenca xml:id="SEQNL_MSG_03">
    <traducao xml:lang="pt-br">Newton</traducao>
    <traducao xml:lang="en-us">Newton</traducao>
  </sentenca>
  <sentenca xml:id="SEQNL_MSG_04">
    <traducao xml:lang="pt-br">Dimensão (número de variáveis): </traducao>
    <traducao xml:lang="en-us">Dimension (number of variables): </traducao>
  </sentenca>
  <sentenca xml:id="SEQNL_MSG_05">
    <traducao xml:lang="pt-br">Número máximo de iterações: </traducao>
    <traducao xml:lang="en-us">Maximum number of iterations: </traducao>
  </sentenca>
  <sentenca xml:id="SEQNL_MSG_06">
    <traducao xml:lang="pt-br">Precisão desejada (digite o valor de k para 10&lt;sup&gt;-&lt;font size=2&gt;k&lt;/sup&gt;&lt;/font&gt;&amp;nbsp): </traducao>
    <traducao xml:lang="en-us">Desired precision (type the value of k for the precision 10&lt;sup&gt;-&lt;font size=2&gt;k&lt;/sup&gt;&lt;/font&gt;&amp;nbsp): </traducao>
  </sentenca>
  <sentenca xml:id="SEQNL_MSG_07">
    <traducao xml:lang="pt-br">Precisão desejada (valor de k para 10&lt;sup&gt;-&lt;font size=2&gt;k&lt;/sup&gt;&lt;/font&gt;&amp;nbsp): </traducao>
    <traducao xml:lang="en-us">Desired precision (value of k for the precision 10&lt;sup&gt;-&lt;font size=2&gt;k&lt;/sup&gt;&lt;/font&gt;&amp;nbsp) </traducao>
  </sentenca>
  <sentenca xml:id="SEQNL_MSG_08">
    <traducao xml:lang="pt-br">Aproximação inicial de X: </traducao>
    <traducao xml:lang="en-us">Initial approache of X: </traducao>
  </sentenca>
  <sentenca xml:id="SEQNL_MSG_09">
    <traducao xml:lang="pt-br">Resposta retirada do arquivo</traducao>
    <traducao xml:lang="en-us">Extracted answer of the archive</traducao>
  </sentenca>
  <sentenca xml:id="SEQNL_MSG_10">
    <traducao xml:lang="pt-br">O método não convergiu.</traducao>
    <traducao xml:lang="en-us">The method did not converge.</traducao>
  </sentenca>
  <sentenca xml:id="SEQNL_MSG_11">
    <traducao xml:lang="pt-br">O método convergiu para: </traducao>
    <traducao xml:lang="en-us">The method converged with: </traducao>
  </sentenca>
  <sentenca xml:id="SEQNL_MSG_12">
    <traducao xml:lang="pt-br">Resposta obtida do arquivo</traducao>
    <traducao xml:lang="en-us">Gotten answer of the archive</traducao>
  </sentenca>
  <sentenca xml:id="SEQNL_MSG_13">
    <traducao xml:lang="pt-br">Sistema</traducao>
    <traducao xml:lang="en-us">System</traducao>
  </sentenca>
  <sentenca xml:id="SEQNL_MSG_14">
    <traducao xml:lang="pt-br">Matriz Jacobiana: </traducao>
    <traducao xml:lang="en-us">Jacobian Matrix: </traducao>
  </sentenca>
  <sentenca xml:id="SEQNL_MSG_15">
    <traducao xml:lang="pt-br">Vetor inicial: </traducao>
    <traducao xml:lang="en-us">Initial vector: </traducao>
  </sentenca>
  <sentenca xml:id="SEQNL_MSG_16">
    <traducao xml:lang="pt-br">Execução do método: </traducao>
    <traducao xml:lang="en-us">Execution of the method: </traducao>
  </sentenca>
  <sentenca xml:id="SEQNL_MSG_17">
    <traducao xml:lang="pt-br">Resposta obtida do programa </traducao>
    <traducao xml:lang="en-us">Gotten answer of the program </traducao>
  </sentenca>
  <sentenca xml:id="SEQNL_MSG_18">
    <traducao xml:lang="pt-br"> iterações.</traducao>
    <traducao xml:lang="en-us"> iterations.</traducao>
  </sentenca>
  <sentenca xml:id="SEQNL_MSG_19">
    <traducao xml:lang="pt-br">Resposta obtida do arquivo</traducao>
    <traducao xml:lang="en-us">Gotten answer of the archive</traducao>
  </sentenca>
  <sentenca xml:id="SEQNL_MSG_20">
    <traducao xml:lang="pt-br">'Testar outras aproximações para x'</traducao>
    <traducao xml:lang="en-us">'Test other approaches to X'</traducao>
  </sentenca>
  <sentenca xml:id="SEQNL_ALGORITMO">
    <traducao xml:lang="pt-br">
        &lt;b&gt;Variáveis: &lt;/b&gt; &lt;br&gt;&lt;br&gt; 
        Auxiliares: &lt;br&gt;
        i, j (contadores), jacob (matriz jacobiana em função das variáveis), mat (matriz jacobiana para um conjunto de pontos x&lt;sub&gt;i&lt;/sub&gt;), parar, cont, f (vetor que armazena os valores das funções f&lt;sub&gt;i&lt;/sub&gt; para um conjunto de pontos x&lt;sub&gt;i&lt;/sub&gt;) &lt;br&gt;&lt;br&gt;
        De entrada: &lt;br&gt;
        dim (dimensão da matriz - número de variáveis), matriz (coeficientes e graus das variáeis do sistema, armazenados respectivamente em 'matriz&lt;sub&gt;coef&lt;/sub&gt;' e 'matriz&lt;sub&gt;grau&lt;/sub&gt;'), k (número de iterações), t (precisão da resposta), vtx (estimativa inicial)  &lt;br&gt;&lt;br&gt;
        De saída: &lt;br&gt;
        vt (vetor resultado - quando o método converge)&lt;br&gt;&lt;br&gt;
        &lt;b&gt;Algoritmo: &lt;/b&gt; &lt;br&gt;&lt;br&gt; 
        função geraJacobiana(matriz,dim) &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; para i de 0 a dim-1 faça &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; para j de 0 a dim-1 faça &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; jacob&lt;sub&gt;&lt;font size=2&gt;i,j,coef&lt;/font&gt;&lt;/sub&gt; := matriz&lt;sub&gt;&lt;font size=2&gt;i,j,coef&lt;/font&gt;&lt;/sub&gt; * matriz&lt;sub&gt;&lt;font size=2&gt;i,j,grau&lt;/font&gt;&lt;/sub&gt; &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; jacob&lt;sub&gt;&lt;font size=2&gt;i,j,grau&lt;/font&gt;&lt;/sub&gt; := matriz&lt;sub&gt;&lt;font size=2&gt;i,j,grau&lt;/font&gt;&lt;/sub&gt; - 1 &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim para &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim para &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; retorna jacob &lt;br&gt;
        fim função &lt;br&gt; &lt;br&gt;
        função atualizaF(matriz,dim,vtx) &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; para i de 0 a dim-1 faça &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; f&lt;sub&gt;&lt;font size=2&gt;i&lt;/font&gt;&lt;/sub&gt; := matriz&lt;sub&gt;&lt;font size=2&gt;i,dim,coef&lt;/font&gt;&lt;/sub&gt; &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim para &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; para i de 0 a dim-1 faça &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; para j de 0 a dim-1 faça &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; f&lt;sub&gt;&lt;font size=2&gt;i&lt;/font&gt;&lt;/sub&gt; := f&lt;sub&gt;&lt;font size=2&gt;i&lt;/font&gt;&lt;/sub&gt; + matriz&lt;sub&gt;&lt;font size=2&gt;i,j,coef&lt;/font&gt;&lt;/sub&gt; * vtx&lt;sub&gt;&lt;font size=2&gt;j&lt;/font&gt;&lt;/sub&gt;&lt;sup&gt;matriz&lt;sub&gt;&lt;font size=2&gt;i,j,grau&lt;/font&gt;&lt;/sub&gt;&lt;/sup&gt; &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim para &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; f&lt;sub&gt;&lt;font size=2&gt;i&lt;/font&gt;&lt;/sub&gt; := -f&lt;sub&gt;&lt;font size=2&gt;i&lt;/font&gt;&lt;/sub&gt; &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim para &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; retorna f &lt;br&gt;
        fim função &lt;br&gt; &lt;br&gt;
        função atualizaJacobiana(jacob,dim,vtx) &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; para i de 0 a dim-1 faça &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; para j de 0 a dim-1 faça &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; mat&lt;sub&gt;&lt;font size=2&gt;i,j&lt;/font&gt;&lt;/sub&gt; := jacob&lt;sub&gt;&lt;font size=2&gt;i,j,coef&lt;/font&gt;&lt;/sub&gt; * vtx&lt;sub&gt;&lt;font size=2&gt;j&lt;/font&gt;&lt;/sub&gt;&lt;sup&gt;jacob&lt;sub&gt;&lt;font size=2&gt;i,j,grau&lt;/font&gt;&lt;/sub&gt;&lt;/sup&gt; &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim para &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim para &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; retorna mat &lt;br&gt;
        fim função &lt;br&gt; &lt;br&gt;
        função convergiu(f,dim,t) &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; convergiu = sim &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; para i de 0 a dim-1 faça &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; se ( f&lt;sub&gt;&lt;font size=2&gt;i&lt;/font&gt;&lt;/sub&gt; * 10&lt;sup&gt;t&lt;/sup&gt; ) é diferente de 0 então &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; convergiu := não &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim se &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim para &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; retorna convergiu &lt;br&gt;
        fim função &lt;br&gt; &lt;br&gt;
        // execução do método &lt;br&gt;
        jacob := geraJacobiana(matriz,dim) &lt;br&gt;
        parar := não &lt;br&gt;
        cont := 0 &lt;br&gt;
        enquanto (parar = não) e (cont &lt;= k) faça &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; f := atualizaF(matriz,dim,vtx) &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; mat := atualizaJacobiana(jacob,dim,vtx)  &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; para i de 0 a dim-1 faça &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; mat&lt;sub&gt;&lt;font size=2&gt;i,dim&lt;/font&gt;&lt;/sub&gt; := f&lt;sub&gt;&lt;font size=2&gt;i&lt;/font&gt;&lt;/sub&gt; &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim para &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; vt := retrosubstituição(triangularização(mat,dim),dim)  &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; /* O procedimento de resolução de sistema de equações lineares  &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; é o método de Eliminação de Gauss */ &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; para i de 0 a dim-1 faça &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; vt&lt;sub&gt;&lt;font size=2&gt;i&lt;/font&gt;&lt;/sub&gt; := vt&lt;sub&gt;&lt;font size=2&gt;i&lt;/font&gt;&lt;/sub&gt; + vtx&lt;sub&gt;&lt;font size=2&gt;i&lt;/font&gt;&lt;/sub&gt; &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim para &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; parar := convergiu(atualizaF(matriz,dim,vt),dim,t) &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; cont := cont + 1 &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; vtx := vt &lt;br&gt;
        fim enquanto &lt;br&gt;
        se parar = sim então &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; 'O método convergiu' &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; retorna vt &lt;br&gt;
        fim se    &lt;br&gt;
        senão se cont = k + 1 então &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; 'O método não convergiu' &lt;br&gt;
        fim senão  </traducao>
    <traducao xml:lang="en-us"/>
  </sentenca>
  <sentenca xml:id="SEQNL_AJUDA">
    <traducao xml:lang="pt-br">
        &lt;ul&gt;
        &lt;li&gt;Os arquivos devem estar no formato .txt&lt;/li&gt; &lt;br&gt;
        &lt;li&gt;Cada linha deve conter apenas &lt;b&gt;um&lt;/b&gt; elemento, na seguinte ordem: &lt;/li&gt; &lt;br&gt;
        &lt;li&gt; &lt;b&gt; Arquivo de dados &lt;/b&gt;
        &lt;br&gt;
        &lt;br&gt; 1ª linha: número de linhas da matriz. &lt;br&gt;
        &lt;br&gt; 2ª linha: número de colunas da matriz. &lt;br&gt;
        &lt;br&gt; Em seguida: valores da matriz A (um por linha), em ordem crescente de coluna e linha. &lt;br&gt;
        &lt;br&gt;
        &lt;li&gt; &lt;b&gt; Arquivo de resposta &lt;/b&gt;
        &lt;br&gt;
        &lt;br&gt; A partir da 1ª linha: elementos da matriz B, em ordem crescente de coluna e linha. &lt;br&gt;
        &lt;/ul&gt;
    </traducao>
    <traducao xml:lang="en-us"/>
  </sentenca>
  <sentenca xml:id="SISTEMAPF_MSG_01">
    <traducao xml:lang="pt-br">Ponto Flutuante</traducao>
    <traducao xml:lang="en-us">Floating Point</traducao>
  </sentenca>
  <sentenca xml:id="SISTEMAPF_MSG_02">
    <traducao xml:lang="pt-br">Aritmética de Ponto Flutuante</traducao>
    <traducao xml:lang="en-us">Arithmetic of floating-point</traducao>
  </sentenca>
  <sentenca xml:id="SISTEMAPF_MSG_03">
    <traducao xml:lang="pt-br">Sistema de Ponto Flutuante</traducao>
    <traducao xml:lang="en-us">Floating point System</traducao>
  </sentenca>
  <sentenca xml:id="SISTEMAPF_MSG_04">
    <traducao xml:lang="pt-br">Este módulo tem como objetivo gerar o conjunto de todos os números de ponto flutuante a partir 
        de um dado sistema de ponto flutuante F(b,m,e&lt;sub&gt;1&lt;/sub&gt;,e&lt;sub&gt;2&lt;/sub&gt;), onde b=base, m=mantissa, e&lt;sub&gt;1&lt;/sub&gt;=expoente inferior e
        e&lt;sub&gt;2&lt;/sub&gt;=expoente superior. 
        Adicionalmente é exibido um gráfico para visualizar a distribuição dos números de ponto flutuante.</traducao>
    <traducao xml:lang="en-us">This module has the objective to generate the set of all
        floating-point numbers from a given system of floating-point F(b,m,e&lt;sub&gt;1&lt;/sub&gt;,e&lt;sub&gt;2&lt;/sub&gt;),
        where b=base, m=mantissa, e&lt;sub&gt;1&lt;/sub&gt;=lower exponent and e&lt;sub&gt;2&lt;/sub&gt;=upper exponent. 
      Additionaly it is shown a graphic to visualize the distribution of the floating-point numbers.</traducao>
  </sentenca>
  <sentenca xml:id="SISTEMAPF_MSG_05">
    <traducao xml:lang="pt-br">Entre com os dados:</traducao>
    <traducao xml:lang="en-us">Type the data:</traducao>
  </sentenca>
  <sentenca xml:id="SISTEMAPF_MSG_06">
    <traducao xml:lang="pt-br">A base b deve estar contida entre 2 e 10.</traducao>
    <traducao xml:lang="en-us">Base b must be between 2 e 10.</traducao>
  </sentenca>
  <sentenca xml:id="SISTEMAPF_MSG_07">
    <traducao xml:lang="pt-br">A mantissa m deve ser maior que 1.</traducao>
    <traducao xml:lang="en-us">A mantissa m must be bigger than 1.</traducao>
  </sentenca>
  <sentenca xml:id="SISTEMAPF_MSG_08">
    <traducao xml:lang="pt-br">e&lt;sub&gt;1&lt;/sub&gt; deve ser menor que e&lt;sub&gt;2&lt;/sub&gt;.</traducao>
    <traducao xml:lang="en-us">e&lt;sub&gt;1&lt;/sub&gt; must be smaller than e&lt;sub&gt;2&lt;/sub&gt;.</traducao>
  </sentenca>
  <sentenca xml:id="SISTEMAPF_MSG_09">
    <traducao xml:lang="pt-br">Informações adicionais</traducao>
    <traducao xml:lang="en-us">Additionaly information</traducao>
  </sentenca>
  <sentenca xml:id="SISTEMAPF_MSG_10">
    <traducao xml:lang="pt-br">número de casas decimais</traducao>
    <traducao xml:lang="en-us">number of decimal houses</traducao>
  </sentenca>
  <sentenca xml:id="SISTEMAPF_MSG_11">
    <traducao xml:lang="pt-br">Cardinalidade:</traducao>
    <traducao xml:lang="en-us">Cardinalidade:</traducao>
  </sentenca>
  <sentenca xml:id="SISTEMAPF_MSG_12">
    <traducao xml:lang="pt-br">Menor número de ponto flutuante</traducao>
    <traducao xml:lang="en-us">Smallest floating-point number</traducao>
  </sentenca>
  <sentenca xml:id="SISTEMAPF_MSG_13">
    <traducao xml:lang="pt-br">Maior número de ponto flutuante</traducao>
    <traducao xml:lang="en-us">Biggest floating-point number</traducao>
  </sentenca>
  <sentenca xml:id="SISTEMAPF_MSG_14">
    <traducao xml:lang="pt-br">Região de underflow</traducao>
    <traducao xml:lang="en-us">Underflow region</traducao>
  </sentenca>
  <sentenca xml:id="SISTEMAPF_MSG_15">
    <traducao xml:lang="pt-br">Região de overflow</traducao>
    <traducao xml:lang="en-us">Overflow region</traducao>
  </sentenca>
  <sentenca xml:id="SISTEMAPF_MSG_16">
    <traducao xml:lang="pt-br">Tabela dos números (em módulo) representáveis</traducao>
    <traducao xml:lang="en-us">Table of the numbers (in module) representable</traducao>
  </sentenca>
  <sentenca xml:id="SISTEMAPF_MSG_17">
    <traducao xml:lang="pt-br">Mantissas</traducao>
    <traducao xml:lang="en-us">Mantissas</traducao>
  </sentenca>
  <sentenca xml:id="SISTEMAPF_MSG_18">
    <traducao xml:lang="pt-br">Distância</traducao>
    <traducao xml:lang="en-us">Distance</traducao>
  </sentenca>
  <sentenca xml:id="SISTEMAPF_MSG_19">
    <traducao xml:lang="pt-br">Gerando os números de ponto flutuante</traducao>
    <traducao xml:lang="en-us">Partial calculations</traducao>
  </sentenca>
  <sentenca xml:id="SISTEMAPF_MSG_20">
    <traducao xml:lang="pt-br">A mantissa do sistema possui precisão de</traducao>
    <traducao xml:lang="en-us">A mantissa do sistema possui precisão de</traducao>
  </sentenca>
  <sentenca xml:id="SISTEMAPF_MSG_21">
    <traducao xml:lang="pt-br">casas decimais.</traducao>
    <traducao xml:lang="en-us">casas decimais.</traducao>
  </sentenca>
  <sentenca xml:id="ARITMETICAPF_AJUDA">
    <traducao xml:lang="pt-br"/>
    <traducao xml:lang="en-us"/>
  </sentenca>
  <sentenca xml:id="SOMA_MSG_01">
    <traducao xml:lang="pt-br">Soma de Matrizes</traducao>
    <traducao xml:lang="en-us">Summation of Matrices</traducao>
  </sentenca>
  <sentenca xml:id="SOMA_MSG_02">
    <traducao xml:lang="pt-br">Aritmética Matricial</traducao>
    <traducao xml:lang="en-us">Matricial Arithmetic</traducao>
  </sentenca>
  <sentenca xml:id="SOMA_MSG_03">
    <traducao xml:lang="pt-br">Soma</traducao>
    <traducao xml:lang="en-us">Summation</traducao>
  </sentenca>
  <sentenca xml:id="SOMA_MSG_04">
    <traducao xml:lang="pt-br">Dimensão:</traducao>
    <traducao xml:lang="en-us">Dimension:</traducao>
  </sentenca>
  <sentenca xml:id="SOMA_MSG_05">
    <traducao xml:lang="pt-br">Matriz A</traducao>
    <traducao xml:lang="en-us">Matrix A</traducao>
  </sentenca>
  <sentenca xml:id="SOMA_MSG_06">
    <traducao xml:lang="pt-br">Matriz B</traducao>
    <traducao xml:lang="en-us">Matrix B</traducao>
  </sentenca>
  <sentenca xml:id="SOMA_MSG_07">
    <traducao xml:lang="pt-br">Matriz C (A + B) - Resposta retirada do arquivo:</traducao>
    <traducao xml:lang="en-us">Matrix C (A + B) - Extracted answer of the archive:</traducao>
  </sentenca>
  <sentenca xml:id="SOMA_MSG_08">
    <traducao xml:lang="pt-br">Matriz C (A + B) - Resposta obtida do programa: </traducao>
    <traducao xml:lang="en-us">Matrix C (A + B) - Gotten answer of the program: </traducao>
  </sentenca>
  <sentenca xml:id="SOMA_ALGORITMO">
    <traducao xml:lang="pt-br">&lt;b&gt;Variáveis: &lt;/b&gt; &lt;br&gt;&lt;br&gt; 
        Auxiliares: &lt;br&gt;
        i e j (contadores) &lt;br&gt;&lt;br&gt;
        De entrada: &lt;br&gt;
        A e B (matrizes), rows (dimensão de linhas das matrizes), cols (dimensão das colunas das matrizes) &lt;br&gt;&lt;br&gt;
        De saída: &lt;br&gt;
        C (matriz) &lt;br&gt;&lt;br&gt;
        &lt;b&gt;Algoritmo: &lt;/b&gt; &lt;br&gt;&lt;br&gt; 
        para i de 0 a rows-1 faça &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; para j de 0 a cols-1 faça &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; C&lt;sub&gt;&lt;font size=2&gt;i,j&lt;/font&gt;&lt;/sub&gt; := A&lt;sub&gt;&lt;font size=2&gt;i,j&lt;/font&gt;&lt;/sub&gt; + B&lt;sub&gt;&lt;font size=2&gt;i,j&lt;/font&gt;&lt;/sub&gt; &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim para j &lt;br&gt;
        fim para i &lt;br&gt;
        retorna C</traducao>
    <traducao xml:lang="en-us"/>
  </sentenca>
  <sentenca xml:id="SOMA_AJUDA">
    <traducao xml:lang="pt-br">&lt;ul&gt;
        &lt;li&gt;Os arquivos devem estar no formato .txt.&lt;/li&gt; &lt;br&gt;
        &lt;li&gt;Cada linha deve conter apenas &lt;b&gt;um&lt;/b&gt; elemento, na seguinte ordem: &lt;/li&gt; &lt;br&gt; 
        &lt;li&gt; &lt;b&gt; Arquivo de dados &lt;/b&gt;
        &lt;br&gt;
        &lt;br&gt; 1ª linha: número de linhas das matrizes. &lt;br&gt;
        &lt;br&gt; 2ª linha: número de colunas das matrizes. &lt;br&gt;
        &lt;br&gt; Em seguida: valores da matriz A, em ordem crescente de coluna e linha. &lt;br&gt;
        &lt;br&gt; Em seguida: valores da matriz B, em ordem crescente de coluna e linha. &lt;br&gt;
        &lt;br&gt;
        &lt;li&gt; &lt;b&gt; Arquivo de resposta &lt;/b&gt;
        &lt;br&gt;
        &lt;br&gt; A partir da 1ª linha: valores da matriz C. &lt;br&gt;
        &lt;/ul&gt;</traducao>
    <traducao xml:lang="en-us"/>
  </sentenca>
  <sentenca xml:id="SOMAPF_MSG_01">
    <traducao xml:lang="pt-br">Ponto Flutuante</traducao>
    <traducao xml:lang="en-us">Floating Point</traducao>
  </sentenca>
  <sentenca xml:id="SOMAPF_MSG_02">
    <traducao xml:lang="pt-br">Aritmética de Ponto Flutuante</traducao>
    <traducao xml:lang="en-us">Floating Point Arithmetic</traducao>
  </sentenca>
  <sentenca xml:id="SOMAPF_MSG_03">
    <traducao xml:lang="pt-br">Soma em Ponto Flutuante</traducao>
    <traducao xml:lang="en-us">Summation</traducao>
  </sentenca>
  <sentenca xml:id="SOMAPF_MSG_04">
    <traducao xml:lang="pt-br">Este módulo tem como objetivo somar dois números em ponto flutuante, a partir 
        de um dado sistema de ponto flutuante F(b,m,e&lt;sub&gt;1&lt;/sub&gt;,e&lt;sub&gt;2&lt;/sub&gt;), onde b=base, m=mantissa, e&lt;sub&gt;1&lt;/sub&gt;=expoente inferior e
        e&lt;sub&gt;2&lt;/sub&gt;=expoente superior.</traducao>
    <traducao xml:lang="en-us">This module has the objective to add two floating-point numbers, from
        a given system of floating-point F(b,m,e&lt;sub&gt;1&lt;/sub&gt;,e&lt;sub&gt;2&lt;/sub&gt;), where b=base, m=,
      e&lt;sub&gt;1&lt;/sub&gt;=lower exponent e e&lt;sub&gt;2&lt;/sub&gt;=upper exponent.</traducao>
  </sentenca>
  <sentenca xml:id="SOMAPF_MSG_05">
    <traducao xml:lang="pt-br">Entre com os dados:</traducao>
    <traducao xml:lang="en-us">Type the data:</traducao>
  </sentenca>
  <sentenca xml:id="SOMAPF_MSG_06">
    <traducao xml:lang="pt-br">A base b deve estar contida entre 2 e 10.</traducao>
    <traducao xml:lang="en-us">Base b must be between 2 and 10.</traducao>
  </sentenca>
  <sentenca xml:id="SOMAPF_MSG_07">
    <traducao xml:lang="pt-br">A mantissa m deve ser maior que 1.</traducao>
    <traducao xml:lang="en-us">A mantissa m deve ser maior que 1.</traducao>
  </sentenca>
  <sentenca xml:id="SOMAPF_MSG_08">
    <traducao xml:lang="pt-br">e&lt;sub&gt;1&lt;/sub&gt; deve ser menor que e&lt;sub&gt;2&lt;/sub&gt;.</traducao>
    <traducao xml:lang="en-us">e&lt;sub&gt;1&lt;/sub&gt; must be smaller than e&lt;sub&gt;2&lt;/sub&gt;.</traducao>
  </sentenca>
  <sentenca xml:id="SOMAPF_MSG_09">
    <traducao xml:lang="pt-br">Resposta retirada do arquivo:</traducao>
    <traducao xml:lang="en-us">Extracted answer of the archive:</traducao>
  </sentenca>
  <sentenca xml:id="SOMAPF_MSG_10">
    <traducao xml:lang="pt-br">Resposta obtida do programa:</traducao>
    <traducao xml:lang="en-us">Gotten answer of the program:</traducao>
  </sentenca>
  <sentenca xml:id="SOMAPF_MSG_11">
    <traducao xml:lang="pt-br">Sistema de ponto flutuante:</traducao>
    <traducao xml:lang="en-us">Floating point system:</traducao>
  </sentenca>
  <sentenca xml:id="SOMAPF_MSG_12">
    <traducao xml:lang="pt-br">Números dados:</traducao>
    <traducao xml:lang="en-us">Given numbers:</traducao>
  </sentenca>
  <sentenca xml:id="SOMAPF_MSG_13">
    <traducao xml:lang="pt-br">Conversão para a base</traducao>
    <traducao xml:lang="en-us">Conversion to base</traducao>
  </sentenca>
  <sentenca xml:id="SOMAPF_MSG_14">
    <traducao xml:lang="pt-br">Normalização e arredondamento dos números:</traducao>
    <traducao xml:lang="en-us">Normalization and rounding of the numbers:</traducao>
  </sentenca>
  <sentenca xml:id="SOMAPF_MSG_15">
    <traducao xml:lang="pt-br">Erro de overflow no expoente:</traducao>
    <traducao xml:lang="en-us">Overflow error in exponent:</traducao>
  </sentenca>
  <sentenca xml:id="SOMAPF_MSG_16">
    <traducao xml:lang="pt-br">Erro de underflow no expoente:</traducao>
    <traducao xml:lang="en-us">Underflow error in exponent:</traducao>
  </sentenca>
  <sentenca xml:id="SOMAPF_MSG_17">
    <traducao xml:lang="pt-br">X&lt;sub&gt;1&lt;/sub&gt; precisa ser maior que X&lt;sub&gt;2&lt;/sub&gt;.</traducao>
    <traducao xml:lang="en-us">X&lt;sub&gt;1&lt;/sub&gt; must be bigger than X&lt;sub&gt;2&lt;/sub&gt;.</traducao>
  </sentenca>
  <sentenca xml:id="SOMAPF_MSG_18">
    <traducao xml:lang="pt-br">Portanto efetua-se a troca dos valores:</traducao>
    <traducao xml:lang="en-us">Therefore is effected the exchange of the values:</traducao>
  </sentenca>
  <sentenca xml:id="SOMAPF_MSG_19">
    <traducao xml:lang="pt-br">Não é possível prosseguir com os cálculos.</traducao>
    <traducao xml:lang="en-us">It is not possible to continue with de calculations.</traducao>
  </sentenca>
  <sentenca xml:id="SOMAPF_MSG_20">
    <traducao xml:lang="pt-br">Cálculo:</traducao>
    <traducao xml:lang="en-us">Calculation:</traducao>
  </sentenca>
  <sentenca xml:id="SOMAPF_MSG_21">
    <traducao xml:lang="pt-br">Para g (diferença entre os expoentes de X&lt;sub&gt;1&lt;/sub&gt; e X&lt;sub&gt;2&lt;/sub&gt;)</traducao>
    <traducao xml:lang="en-us">For g (difference between the exponents of X&lt;sub&gt;1&lt;/sub&gt; e X&lt;sub&gt;2&lt;/sub&gt;)</traducao>
  </sentenca>
  <sentenca xml:id="SOMAPF_MSG_22">
    <traducao xml:lang="pt-br">(mantissa do sistema F) então:</traducao>
    <traducao xml:lang="en-us">(mantissa of system F) then:</traducao>
  </sentenca>
  <sentenca xml:id="SOMAPF_MSG_23">
    <traducao xml:lang="pt-br">Mantissas dos números:</traducao>
    <traducao xml:lang="en-us">Mantissas of the numbers:</traducao>
  </sentenca>
  <sentenca xml:id="SOMAPF_MSG_24">
    <traducao xml:lang="pt-br">Alinhar x&lt;sub&gt;2&lt;/sub&gt; de</traducao>
    <traducao xml:lang="en-us">Align x&lt;sub&gt;2&lt;/sub&gt; of</traducao>
  </sentenca>
  <sentenca xml:id="SOMAPF_MSG_25">
    <traducao xml:lang="pt-br">posições à direita.</traducao>
    <traducao xml:lang="en-us">positions to the right.</traducao>
  </sentenca>
  <sentenca xml:id="SOMAPF_MSG_26">
    <traducao xml:lang="pt-br">Efetuar a soma dos números, agora ambos com expoente</traducao>
    <traducao xml:lang="en-us">Effect the addition of the numbers, now both with the exponent</traducao>
  </sentenca>
  <sentenca xml:id="SOMAPF_MSG_27">
    <traducao xml:lang="pt-br">soma</traducao>
    <traducao xml:lang="en-us">summation</traducao>
  </sentenca>
  <sentenca xml:id="SOMAPF_MSG_28">
    <traducao xml:lang="pt-br">Normalização e arredondamento da resposta:</traducao>
    <traducao xml:lang="en-us">Normalization and rounding of the answer:</traducao>
  </sentenca>
  <sentenca xml:id="SOMAPF_MSG_29">
    <traducao xml:lang="pt-br">O número já está normalizado.</traducao>
    <traducao xml:lang="en-us">The number is already normalizated.</traducao>
  </sentenca>
  <sentenca xml:id="SOMAPF_MSG_30">
    <traducao xml:lang="pt-br">A resposta obtida não pertence ao sistema F dado.</traducao>
    <traducao xml:lang="en-us">The gotten answer does not belong at this F system.</traducao>
  </sentenca>
  <sentenca xml:id="SOMAPF_MSG_31">
    <traducao xml:lang="pt-br">em decimal</traducao>
    <traducao xml:lang="en-us">in decimal</traducao>
  </sentenca>
  <sentenca xml:id="SUBPF_MSG_01">
    <traducao xml:lang="pt-br">Ponto Flutuante</traducao>
    <traducao xml:lang="en-us">Floating Point</traducao>
  </sentenca>
  <sentenca xml:id="SUBPF_MSG_02">
    <traducao xml:lang="pt-br">Aritmética de Ponto Flutuante</traducao>
    <traducao xml:lang="en-us">Floating Point Arithmetic</traducao>
  </sentenca>
  <sentenca xml:id="SUBPF_MSG_03">
    <traducao xml:lang="pt-br">Subtração em Ponto Flutuante</traducao>
    <traducao xml:lang="en-us">Subtraction</traducao>
  </sentenca>
  <sentenca xml:id="SUBPF_MSG_04">
    <traducao xml:lang="pt-br">Este módulo tem como objetivo subtrair dois números em ponto flutuante, a partir 
        de um dado sistema de ponto flutuante F(b,m,e&lt;sub&gt;1&lt;/sub&gt;,e&lt;sub&gt;2&lt;/sub&gt;), onde b=base, m=mantissa, e&lt;sub&gt;1&lt;/sub&gt;=expoente inferior e
        e&lt;sub&gt;2&lt;/sub&gt;=expoente superior. &lt;/p&gt;&lt;p&gt; Note que os números de entrada devem ser positivos, pois o sinal de menos é tradado como
        um &lt;b&gt; operador &lt;/b&gt;.</traducao>
    <traducao xml:lang="en-us">This module has the objective to subtract two floating-point numbers, from
        a given system of floating-point F(b,m,e&lt;sub&gt;1&lt;/sub&gt;,e&lt;sub&gt;2&lt;/sub&gt;), where b=base, m=,
        e&lt;sub&gt;1&lt;/sub&gt;=lower exponent e e&lt;sub&gt;2&lt;/sub&gt;=upper exponent. 
    &lt;/p&gt;&lt;p&gt; Note that the given numbers must be positive, because the signal '-' is treated
      like an &lt;b&gt; operator &lt;/b&gt;.</traducao>
  </sentenca>
  <sentenca xml:id="SUBPF_MSG_05">
    <traducao xml:lang="pt-br">Entre com os dados:</traducao>
    <traducao xml:lang="en-us">Type the data:</traducao>
  </sentenca>
  <sentenca xml:id="SUBPF_MSG_06">
    <traducao xml:lang="pt-br">A base b deve estar contida entre 2 e 10.</traducao>
    <traducao xml:lang="en-us">Base b must be between 2 and 10.</traducao>
  </sentenca>
  <sentenca xml:id="SUBPF_MSG_07">
    <traducao xml:lang="pt-br">A mantissa m deve ser maior que 1.</traducao>
    <traducao xml:lang="en-us">A mantissa m deve ser maior que 1.</traducao>
  </sentenca>
  <sentenca xml:id="SUBPF_MSG_08">
    <traducao xml:lang="pt-br">e&lt;sub&gt;1&lt;/sub&gt; deve ser menor que e&lt;sub&gt;2&lt;/sub&gt;.</traducao>
    <traducao xml:lang="en-us">e&lt;sub&gt;1&lt;/sub&gt; must be smaller than e&lt;sub&gt;2&lt;/sub&gt;.</traducao>
  </sentenca>
  <sentenca xml:id="SUBPF_MSG_09">
    <traducao xml:lang="pt-br">Resposta retirada do arquivo:</traducao>
    <traducao xml:lang="en-us">Extracted answer of the archive:</traducao>
  </sentenca>
  <sentenca xml:id="SUBPF_MSG_10">
    <traducao xml:lang="pt-br">Resposta obtida do programa:</traducao>
    <traducao xml:lang="en-us">Gotten answer of the program:</traducao>
  </sentenca>
  <sentenca xml:id="SUBPF_MSG_11">
    <traducao xml:lang="pt-br">Sistema de ponto flutuante:</traducao>
    <traducao xml:lang="en-us">Floating point system</traducao>
  </sentenca>
  <sentenca xml:id="SUBPF_MSG_12">
    <traducao xml:lang="pt-br">Números dados:</traducao>
    <traducao xml:lang="en-us">Given numbers:</traducao>
  </sentenca>
  <sentenca xml:id="SUBPF_MSG_13">
    <traducao xml:lang="pt-br">Conversão para a base</traducao>
    <traducao xml:lang="en-us">Conversion to base</traducao>
  </sentenca>
  <sentenca xml:id="SUBPF_MSG_14">
    <traducao xml:lang="pt-br">Normalização e arredondamento dos números:</traducao>
    <traducao xml:lang="en-us">Normalization and rounding of the numbers:</traducao>
  </sentenca>
  <sentenca xml:id="SUBPF_MSG_15">
    <traducao xml:lang="pt-br">Erro de overflow no expoente:</traducao>
    <traducao xml:lang="en-us">Overflow error in exponent:</traducao>
  </sentenca>
  <sentenca xml:id="SUBPF_MSG_16">
    <traducao xml:lang="pt-br">Erro de underflow no expoente:</traducao>
    <traducao xml:lang="en-us">Underflow error in exponent:</traducao>
  </sentenca>
  <sentenca xml:id="SUBPF_MSG_17">
    <traducao xml:lang="pt-br">X&lt;sub&gt;1&lt;/sub&gt; precisa ser maior que X&lt;sub&gt;2&lt;/sub&gt;.</traducao>
    <traducao xml:lang="en-us">X&lt;sub&gt;1&lt;/sub&gt; must be bigger than X&lt;sub&gt;2&lt;/sub&gt;.</traducao>
  </sentenca>
  <sentenca xml:id="SUBPF_MSG_18">
    <traducao xml:lang="pt-br">Portanto efetua-se a troca dos valores:</traducao>
    <traducao xml:lang="en-us">Therefore is effected the exchange of the values:</traducao>
  </sentenca>
  <sentenca xml:id="SUBPF_MSG_19">
    <traducao xml:lang="pt-br">Não é possível prosseguir com os cálculos.</traducao>
    <traducao xml:lang="en-us">t is not possible to continue with de calculations.</traducao>
  </sentenca>
  <sentenca xml:id="SUBPF_MSG_20">
    <traducao xml:lang="pt-br">Cálculo:</traducao>
    <traducao xml:lang="en-us">Calculation:</traducao>
  </sentenca>
  <sentenca xml:id="SUBPF_MSG_21">
    <traducao xml:lang="pt-br">Para g (diferença entre os expoentes de X&lt;sub&gt;1&lt;/sub&gt; e X&lt;sub&gt;2&lt;/sub&gt;)</traducao>
    <traducao xml:lang="en-us">For g (difference between the exponents of X&lt;sub&gt;1&lt;/sub&gt; e X&lt;sub&gt;2&lt;/sub&gt;)</traducao>
  </sentenca>
  <sentenca xml:id="SUBPF_MSG_22">
    <traducao xml:lang="pt-br">(mantissa do sistema F) então:</traducao>
    <traducao xml:lang="en-us">(mantissa of system F) then:</traducao>
  </sentenca>
  <sentenca xml:id="SUBPF_MSG_23">
    <traducao xml:lang="pt-br">Mantissas dos números:</traducao>
    <traducao xml:lang="en-us">Mantissas of the numbers:</traducao>
  </sentenca>
  <sentenca xml:id="SUBPF_MSG_24">
    <traducao xml:lang="pt-br">Alinhar x&lt;sub&gt;2&lt;/sub&gt; de</traducao>
    <traducao xml:lang="en-us">Align x&lt;sub&gt;2&lt;/sub&gt; of</traducao>
  </sentenca>
  <sentenca xml:id="SUBPF_MSG_25">
    <traducao xml:lang="pt-br">posições à direita.</traducao>
    <traducao xml:lang="en-us">positions to the right.</traducao>
  </sentenca>
  <sentenca xml:id="SUBPF_MSG_26">
    <traducao xml:lang="pt-br">Efetuar a soma dos números, agora ambos com expoente</traducao>
    <traducao xml:lang="en-us">Effect the subtraction of the numbers, now both with the exponent</traducao>
  </sentenca>
  <sentenca xml:id="SUBPF_MSG_27">
    <traducao xml:lang="pt-br">soma</traducao>
    <traducao xml:lang="en-us">sub</traducao>
  </sentenca>
  <sentenca xml:id="SUBPF_MSG_28">
    <traducao xml:lang="pt-br">Normalização e arredondamento da resposta:</traducao>
    <traducao xml:lang="en-us">Normalization and rounding of the answer:</traducao>
  </sentenca>
  <sentenca xml:id="SUBPF_MSG_29">
    <traducao xml:lang="pt-br">O número já está normalizado.</traducao>
    <traducao xml:lang="en-us">The number is already normalizated.</traducao>
  </sentenca>
  <sentenca xml:id="SUBPF_MSG_30">
    <traducao xml:lang="pt-br">A resposta obtida não pertence ao sistema F dado.</traducao>
    <traducao xml:lang="en-us">The gotten answer does not belong at this F system.</traducao>
  </sentenca>
  <sentenca xml:id="SUBPF_MSG_31">
    <traducao xml:lang="pt-br">em decimal</traducao>
    <traducao xml:lang="en-us">in decimal</traducao>
  </sentenca>
  <sentenca xml:id="SUBPF_MSG_32">
    <traducao xml:lang="pt-br">Então a operação a ser realizada é:</traducao>
    <traducao xml:lang="en-us">Then the operation that must be done is:</traducao>
  </sentenca>
  <sentenca xml:id="MULTPF_MSG_01">
    <traducao xml:lang="pt-br">Ponto Flutuante</traducao>
    <traducao xml:lang="en-us">Floating Point</traducao>
  </sentenca>
  <sentenca xml:id="MULTPF_MSG_02">
    <traducao xml:lang="pt-br">Aritmética de Ponto Flutuante</traducao>
    <traducao xml:lang="en-us">Arithmetic of Floating Point</traducao>
  </sentenca>
  <sentenca xml:id="MULTPF_MSG_03">
    <traducao xml:lang="pt-br">Multiplicação em Ponto Flutuante</traducao>
    <traducao xml:lang="en-us">Multiplication</traducao>
  </sentenca>
  <sentenca xml:id="MULTPF_MSG_04">
    <traducao xml:lang="pt-br">Este módulo tem como objetivo multiplicar dois números em ponto flutuante, a partir 
        de um dado sistema de ponto flutuante F(b,m,e&lt;sub&gt;1&lt;/sub&gt;,e&lt;sub&gt;2&lt;/sub&gt;), onde b=base, m=mantissa, e&lt;sub&gt;1&lt;/sub&gt;=expoente inferior e
        e&lt;sub&gt;2&lt;/sub&gt;=expoente superior.</traducao>
    <traducao xml:lang="en-us">This module has the objective to multiply two floating-point numbers, from
        a given system of floating-point F(b,m,e&lt;sub&gt;1&lt;/sub&gt;,e&lt;sub&gt;2&lt;/sub&gt;), where b=base, m=,
      e&lt;sub&gt;1&lt;/sub&gt;=lower exponent e e&lt;sub&gt;2&lt;/sub&gt;=upper exponent.</traducao>
  </sentenca>
  <sentenca xml:id="MULTPF_MSG_05">
    <traducao xml:lang="pt-br">Entre com os dados:</traducao>
    <traducao xml:lang="en-us">Type the data:</traducao>
  </sentenca>
  <sentenca xml:id="MULTPF_MSG_06">
    <traducao xml:lang="pt-br">A base b deve estar contida entre 2 e 10.</traducao>
    <traducao xml:lang="en-us">Base b must be between 2 and 10.</traducao>
  </sentenca>
  <sentenca xml:id="MULTPF_MSG_07">
    <traducao xml:lang="pt-br">A mantissa m deve ser maior que 1.</traducao>
    <traducao xml:lang="en-us">A mantissa m deve ser maior que 1.</traducao>
  </sentenca>
  <sentenca xml:id="MULTPF_MSG_08">
    <traducao xml:lang="pt-br">e&lt;sub&gt;1&lt;/sub&gt; deve ser menor que e&lt;sub&gt;2&lt;/sub&gt;.</traducao>
    <traducao xml:lang="en-us">e&lt;sub&gt;1&lt;/sub&gt; must be smaller than e&lt;sub&gt;2&lt;/sub&gt;.</traducao>
  </sentenca>
  <sentenca xml:id="MULTPF_MSG_09">
    <traducao xml:lang="pt-br">Resposta retirada do arquivo:</traducao>
    <traducao xml:lang="en-us">Extracted answer of the archive:</traducao>
  </sentenca>
  <sentenca xml:id="MULTPF_MSG_10">
    <traducao xml:lang="pt-br">Resposta obtida do programa:</traducao>
    <traducao xml:lang="en-us">Gotten answer of the program:</traducao>
  </sentenca>
  <sentenca xml:id="MULTPF_MSG_11">
    <traducao xml:lang="pt-br">Sistema de ponto flutuante:</traducao>
    <traducao xml:lang="en-us">System of floating point:</traducao>
  </sentenca>
  <sentenca xml:id="MULTPF_MSG_12">
    <traducao xml:lang="pt-br">Números dados:</traducao>
    <traducao xml:lang="en-us">Given numbers:</traducao>
  </sentenca>
  <sentenca xml:id="MULTPF_MSG_13">
    <traducao xml:lang="pt-br">Conversão para a base</traducao>
    <traducao xml:lang="en-us">Conversion to base</traducao>
  </sentenca>
  <sentenca xml:id="MULTPF_MSG_14">
    <traducao xml:lang="pt-br">Normalização e arredondamento dos números:</traducao>
    <traducao xml:lang="en-us">Normalization and rounding of the numbers:</traducao>
  </sentenca>
  <sentenca xml:id="MULTPF_MSG_15">
    <traducao xml:lang="pt-br">Erro de overflow no expoente:</traducao>
    <traducao xml:lang="en-us">Overflow error in exponent:</traducao>
  </sentenca>
  <sentenca xml:id="MULTPF_MSG_16">
    <traducao xml:lang="pt-br">Erro de underflow no expoente:</traducao>
    <traducao xml:lang="en-us">Underflow error in exponent:</traducao>
  </sentenca>
  <sentenca xml:id="MULTPF_MSG_17">
    <traducao xml:lang="pt-br">Não é possível prosseguir com os cálculos.</traducao>
    <traducao xml:lang="en-us">It is not possible to continue with de calculations.</traducao>
  </sentenca>
  <sentenca xml:id="MULTPF_MSG_18">
    <traducao xml:lang="pt-br">Cálculo:</traducao>
    <traducao xml:lang="en-us">Calculation:</traducao>
  </sentenca>
  <sentenca xml:id="MULTPF_MSG_19">
    <traducao xml:lang="pt-br">Multiplique</traducao>
    <traducao xml:lang="en-us">Multiply</traducao>
  </sentenca>
  <sentenca xml:id="MULTPF_MSG_20">
    <traducao xml:lang="pt-br">e some seus expoentes:</traducao>
    <traducao xml:lang="en-us">and add its exponents:</traducao>
  </sentenca>
  <sentenca xml:id="MULTPF_MSG_21">
    <traducao xml:lang="pt-br">Portanto temos:</traducao>
    <traducao xml:lang="en-us">Therefore we have:</traducao>
  </sentenca>
  <sentenca xml:id="MULTPF_MSG_22">
    <traducao xml:lang="pt-br">Normalização e arredondamento da resposta:</traducao>
    <traducao xml:lang="en-us">Normalization and rounding of the answer:</traducao>
  </sentenca>
  <sentenca xml:id="MULTPF_MSG_23">
    <traducao xml:lang="pt-br">O número já está normalizado.</traducao>
    <traducao xml:lang="en-us">The number is already normalizated.</traducao>
  </sentenca>
  <sentenca xml:id="MULTPF_MSG_24">
    <traducao xml:lang="pt-br">A resposta obtida não pertence ao sistema F dado.</traducao>
    <traducao xml:lang="en-us">The gotten answer does not belong at this F system.</traducao>
  </sentenca>
  <sentenca xml:id="MULTPF_MSG_31">
    <traducao xml:lang="pt-br">em decimal</traducao>
    <traducao xml:lang="en-us">in decimal</traducao>
  </sentenca>
  <sentenca xml:id="DIVPF_MSG_01">
    <traducao xml:lang="pt-br">Ponto Flutuante</traducao>
    <traducao xml:lang="en-us">Floating Point</traducao>
  </sentenca>
  <sentenca xml:id="DIVPF_MSG_02">
    <traducao xml:lang="pt-br">Aritmética de Ponto Flutuante</traducao>
    <traducao xml:lang="en-us">Arithmetic of Floating Point</traducao>
  </sentenca>
  <sentenca xml:id="DIVPF_MSG_03">
    <traducao xml:lang="pt-br">Divisão em Ponto Flutuante</traducao>
    <traducao xml:lang="en-us">Division</traducao>
  </sentenca>
  <sentenca xml:id="DIVPF_MSG_04">
    <traducao xml:lang="pt-br">Este módulo tem como objetivo dividir dois números em ponto flutuante, a partir 
        de um dado sistema de ponto flutuante F(b,m,e&lt;sub&gt;1&lt;/sub&gt;,e&lt;sub&gt;2&lt;/sub&gt;), onde b=base, m=mantissa, e&lt;sub&gt;1&lt;/sub&gt;=expoente inferior e
        e&lt;sub&gt;2&lt;/sub&gt;=expoente superior.</traducao>
    <traducao xml:lang="en-us">This module has the objective to divide two floating-point numbers, from
        a given system of floating-point F(b,m,e&lt;sub&gt;1&lt;/sub&gt;,e&lt;sub&gt;2&lt;/sub&gt;), where b=base, m=,
      e&lt;sub&gt;1&lt;/sub&gt;=lower exponent e e&lt;sub&gt;2&lt;/sub&gt;=upper exponent.</traducao>
  </sentenca>
  <sentenca xml:id="DIVPF_MSG_05">
    <traducao xml:lang="pt-br">Entre com os dados:</traducao>
    <traducao xml:lang="en-us">Type the data:</traducao>
  </sentenca>
  <sentenca xml:id="DIVPF_MSG_06">
    <traducao xml:lang="pt-br">A base b deve estar contida entre 2 e 10.</traducao>
    <traducao xml:lang="en-us">Base b must be between 2 and 10.</traducao>
  </sentenca>
  <sentenca xml:id="DIVPF_MSG_07">
    <traducao xml:lang="pt-br">A mantissa m deve ser maior que 1.</traducao>
    <traducao xml:lang="en-us">A mantissa m deve ser maior que 1.</traducao>
  </sentenca>
  <sentenca xml:id="DIVPF_MSG_08">
    <traducao xml:lang="pt-br">e&lt;sub&gt;1&lt;/sub&gt; deve ser menor que e&lt;sub&gt;2&lt;/sub&gt;.</traducao>
    <traducao xml:lang="en-us">e&lt;sub&gt;1&lt;/sub&gt; must be smaller than e&lt;sub&gt;2&lt;/sub&gt;.</traducao>
  </sentenca>
  <sentenca xml:id="DIVPF_MSG_09">
    <traducao xml:lang="pt-br">Resposta retirada do arquivo:</traducao>
    <traducao xml:lang="en-us">Extracted answer of the archive:</traducao>
  </sentenca>
  <sentenca xml:id="DIVPF_MSG_10">
    <traducao xml:lang="pt-br">Resposta obtida do programa:</traducao>
    <traducao xml:lang="en-us">Gotten answer of the program:</traducao>
  </sentenca>
  <sentenca xml:id="DIVPF_MSG_11">
    <traducao xml:lang="pt-br">Sistema de ponto flutuante:</traducao>
    <traducao xml:lang="en-us">System of floating point:</traducao>
  </sentenca>
  <sentenca xml:id="DIVPF_MSG_12">
    <traducao xml:lang="pt-br">Números dados:</traducao>
    <traducao xml:lang="en-us">Given numbers:</traducao>
  </sentenca>
  <sentenca xml:id="DIVPF_MSG_13">
    <traducao xml:lang="pt-br">Conversão para a base</traducao>
    <traducao xml:lang="en-us">Conversion to base</traducao>
  </sentenca>
  <sentenca xml:id="DIVPF_MSG_14">
    <traducao xml:lang="pt-br">Normalização e arredondamento dos números:</traducao>
    <traducao xml:lang="en-us">Normalization and rounding of the numbers:</traducao>
  </sentenca>
  <sentenca xml:id="DIVPF_MSG_15">
    <traducao xml:lang="pt-br">Erro de overflow no expoente:</traducao>
    <traducao xml:lang="en-us">Overflow error in exponent:</traducao>
  </sentenca>
  <sentenca xml:id="DIVPF_MSG_16">
    <traducao xml:lang="pt-br">Erro de underflow no expoente:</traducao>
    <traducao xml:lang="en-us">Underflow error in exponent:</traducao>
  </sentenca>
  <sentenca xml:id="DIVPF_MSG_17">
    <traducao xml:lang="pt-br">Não é possível prosseguir com os cálculos.</traducao>
    <traducao xml:lang="en-us">It is not possible to continue with de calculations.</traducao>
  </sentenca>
  <sentenca xml:id="DIVPF_MSG_18">
    <traducao xml:lang="pt-br">Cálculo:</traducao>
    <traducao xml:lang="en-us">Calculation:</traducao>
  </sentenca>
  <sentenca xml:id="DIVPF_MSG_19">
    <traducao xml:lang="pt-br">Divida</traducao>
    <traducao xml:lang="en-us">Divide</traducao>
  </sentenca>
  <sentenca xml:id="DIVPF_MSG_20">
    <traducao xml:lang="pt-br">e subtraia seus expoentes:</traducao>
    <traducao xml:lang="en-us">and subtract its exponents:</traducao>
  </sentenca>
  <sentenca xml:id="DIVPF_MSG_21">
    <traducao xml:lang="pt-br">Portanto temos:</traducao>
    <traducao xml:lang="en-us">Therefore we have:</traducao>
  </sentenca>
  <sentenca xml:id="DIVPF_MSG_22">
    <traducao xml:lang="pt-br">Normalização e arredondamento da resposta:</traducao>
    <traducao xml:lang="en-us">Normalization and rounding of the answer:</traducao>
  </sentenca>
  <sentenca xml:id="DIVPF_MSG_23">
    <traducao xml:lang="pt-br">O número já está normalizado.</traducao>
    <traducao xml:lang="en-us">The number is already normalizated.</traducao>
  </sentenca>
  <sentenca xml:id="DIVPF_MSG_24">
    <traducao xml:lang="pt-br">A resposta obtida não pertence ao sistema F dado.</traducao>
    <traducao xml:lang="en-us">The gotten answer does not belong at this F system.</traducao>
  </sentenca>
  <sentenca xml:id="DIVPF_MSG_31">
    <traducao xml:lang="pt-br">em decimal</traducao>
    <traducao xml:lang="en-us">in decimal</traducao>
  </sentenca>
  <sentenca xml:id="SPLINE_MSG_01">
    <traducao xml:lang="pt-br">Splines cúbicos</traducao>
    <traducao xml:lang="en-us">Cubic Splines</traducao>
  </sentenca>
  <sentenca xml:id="SPLINE_MSG_02">
    <traducao xml:lang="pt-br">Interpolação Polinomial</traducao>
    <traducao xml:lang="en-us">Polynomial Interpolation</traducao>
  </sentenca>
  <sentenca xml:id="SPLINE_MSG_03">
    <traducao xml:lang="pt-br">Splines</traducao>
    <traducao xml:lang="en-us">Splines</traducao>
  </sentenca>
  <sentenca xml:id="SPLINE_MSG_04">
    <traducao xml:lang="pt-br">Selecione uma opção para entrada de dados:</traducao>
    <traducao xml:lang="en-us">Select an option of problem:</traducao>
  </sentenca>
  <sentenca xml:id="SPLINE_MSG_05">
    <traducao xml:lang="pt-br">Caso discreto (através de um conjunto de pontos)</traducao>
    <traducao xml:lang="en-us">Discrete case (through a set of points)</traducao>
  </sentenca>
  <sentenca xml:id="SPLINE_MSG_06">
    <traducao xml:lang="pt-br">Caso contínuo (através de uma função e um intervalo)</traducao>
    <traducao xml:lang="en-us">Continuous case (through a function and a interval)</traducao>
  </sentenca>
  <sentenca xml:id="SPLINE_MSG_07">
    <traducao xml:lang="pt-br">Digite o número de pontos que serão dados como entrada: </traducao>
    <traducao xml:lang="en-us">Type the number of points that will be given as entry: </traducao>
  </sentenca>
  <sentenca xml:id="SPLINE_MSG_09">
    <traducao xml:lang="pt-br">Digite a função: </traducao>
    <traducao xml:lang="en-us">Type the function: </traducao>
  </sentenca>
  <sentenca xml:id="SPLINE_MSG_10">
    <traducao xml:lang="pt-br">Digite o intervalo em que a função será aproximada: </traducao>
    <traducao xml:lang="en-us">Type the interval where the function will be aproached: </traducao>
  </sentenca>
  <sentenca xml:id="SPLINE_MSG_11">
    <traducao xml:lang="pt-br">Tipo de distribuição dos </traducao>
    <traducao xml:lang="en-us">Type of distribution of the </traducao>
  </sentenca>
  <sentenca xml:id="SPLINE_MSG_12">
    <traducao xml:lang="pt-br"> pontos no intervalo </traducao>
    <traducao xml:lang="en-us"> points of the interval </traducao>
  </sentenca>
  <sentenca xml:id="SPLINE_MSG_13">
    <traducao xml:lang="pt-br">Distribuição uniforme</traducao>
    <traducao xml:lang="en-us">Uniform distribution</traducao>
  </sentenca>
  <sentenca xml:id="SPLINE_MSG_14">
    <traducao xml:lang="pt-br">Distribuição de Chebyshev</traducao>
    <traducao xml:lang="en-us">Chebyshev distribution</traducao>
  </sentenca>
  <sentenca xml:id="SPLINE_MSG_15">
    <traducao xml:lang="pt-br">Número de pontos:</traducao>
    <traducao xml:lang="en-us">Number of points:</traducao>
  </sentenca>
  <sentenca xml:id="SPLINE_MSG_16">
    <traducao xml:lang="pt-br">Grau do polinômio p(x): </traducao>
    <traducao xml:lang="en-us">Degree of the polynomial p(x) </traducao>
  </sentenca>
  <sentenca xml:id="SPLINE_MSG_17">
    <traducao xml:lang="pt-br">Função dada:</traducao>
    <traducao xml:lang="en-us">Given function:</traducao>
  </sentenca>
  <sentenca xml:id="SPLINE_MSG_18">
    <traducao xml:lang="pt-br">Intervalo </traducao>
    <traducao xml:lang="en-us">Interval </traducao>
  </sentenca>
  <sentenca xml:id="SPLINE_MSG_19">
    <traducao xml:lang="pt-br">Valores conhecidos:</traducao>
    <traducao xml:lang="en-us">Known values:</traducao>
  </sentenca>
  <sentenca xml:id="SPLINE_MSG_20">
    <traducao xml:lang="pt-br">Calcular p(x) para x= </traducao>
    <traducao xml:lang="en-us">Calculate p(x) to x= </traducao>
  </sentenca>
  <sentenca xml:id="SPLINE_MSG_21">
    <traducao xml:lang="pt-br">Resposta retirada do arquivo: </traducao>
    <traducao xml:lang="en-us">Extracted answer of the archive: </traducao>
  </sentenca>
  <sentenca xml:id="SPLINE_MSG_22">
    <traducao xml:lang="pt-br">Resposta obtida do programa: </traducao>
    <traducao xml:lang="en-us">Gotten answer of the program: </traducao>
  </sentenca>
  <sentenca xml:id="SPLINE_MSG_23">
    <traducao xml:lang="pt-br">Resposta obtida do arquivo: </traducao>
    <traducao xml:lang="en-us">Gotten answer of the archive: </traducao>
  </sentenca>
  <sentenca xml:id="SPLINE_MSG_24">
    <traducao xml:lang="pt-br">O valor </traducao>
    <traducao xml:lang="en-us">The value </traducao>
  </sentenca>
  <sentenca xml:id="SPLINE_MSG_25">
    <traducao xml:lang="pt-br"> para x deve estar contido no intervalo </traducao>
    <traducao xml:lang="en-us"> to x must be between the interval </traducao>
  </sentenca>
  <sentenca xml:id="SPLINE_MSG_26">
    <traducao xml:lang="pt-br">'Calcular para outro ponto'</traducao>
    <traducao xml:lang="en-us">'Type another value'</traducao>
  </sentenca>
  <sentenca xml:id="SPLINE_MSG_27">
    <traducao xml:lang="pt-br">Polinômio Interpolador no intevalo </traducao>
    <traducao xml:lang="en-us">Polynomial of the interval </traducao>
  </sentenca>
  <sentenca xml:id="SPLINE_MSG_28">
    <traducao xml:lang="pt-br">Calculado para x = </traducao>
    <traducao xml:lang="en-us">Calculated where x = </traducao>
  </sentenca>
  <sentenca xml:id="SPLINE_MSG_29">
    <traducao xml:lang="pt-br">Correção de resposta do arquivo</traducao>
    <traducao xml:lang="en-us">Gotten answer of the archive</traducao>
  </sentenca>
  <sentenca xml:id="SPLINE_MSG_30">
    <traducao xml:lang="pt-br">Polinômio interpolador da solução, no intervalo </traducao>
    <traducao xml:lang="en-us">Polynomial of the solution, in the interval </traducao>
  </sentenca>
  <sentenca xml:id="SPLINE_MSG_31">
    <traducao xml:lang="pt-br">Polinômios definidos nos demais intervalos</traducao>
    <traducao xml:lang="en-us">Polynomials defined in others intervals</traducao>
  </sentenca>
  <sentenca xml:id="SPLINE_MSG_32">
    <traducao xml:lang="pt-br">, obtidos pelo programa: </traducao>
    <traducao xml:lang="en-us">, gotten of the program: </traducao>
  </sentenca>
  <sentenca xml:id="SPLINE_MSG_33">
    <traducao xml:lang="pt-br">Para x= </traducao>
    <traducao xml:lang="en-us">For x= </traducao>
  </sentenca>
  <sentenca xml:id="SPLINE_ALGORITMO">
    <traducao xml:lang="pt-br">
        &lt;b&gt;Variáveis: &lt;/b&gt; &lt;br&gt;&lt;br&gt; 
        Auxiliares: &lt;br&gt;
        i, j (contadores), b, c, d, h, o, alpha, beta, gama (vetores), aux, diferenca, xo &lt;br&gt;&lt;br&gt;
        De entrada: &lt;br&gt;
        n (número de pontos), x e y (vetores), valor (ponto a ser interpolado)  &lt;br&gt;&lt;br&gt;
        De saída: &lt;br&gt;
        solucao (resultado da interpolação no ponto 'valor')&lt;br&gt;&lt;br&gt;
        &lt;b&gt;Algoritmo: &lt;/b&gt; &lt;br&gt;&lt;br&gt; 
        // ordena o conjunto de pontos na ordem crescente dos valores de x &lt;br&gt;
        para tam de n a 2 faça &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; para i de 0 a tam-2 faça &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; se  x&lt;sub&gt;&lt;font size=2&gt;i&lt;/font&gt;&lt;/sub&gt; &gt; x&lt;sub&gt;&lt;font size=2&gt;i+1&lt;/font&gt;&lt;/sub&gt; então &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; aux := x&lt;sub&gt;&lt;font size=2&gt;i&lt;/font&gt;&lt;/sub&gt; &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; x&lt;sub&gt;&lt;font size=2&gt;i&lt;/font&gt;&lt;/sub&gt; := x&lt;sub&gt;&lt;font size=2&gt;i+1&lt;/font&gt;&lt;/sub&gt; &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; x&lt;sub&gt;&lt;font size=2&gt;i+1&lt;/font&gt;&lt;/sub&gt; := aux &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; aux := y&lt;sub&gt;&lt;font size=2&gt;i&lt;/font&gt;&lt;/sub&gt; &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; y&lt;sub&gt;&lt;font size=2&gt;i&lt;/font&gt;&lt;/sub&gt; := y&lt;sub&gt;&lt;font size=2&gt;i+1&lt;/font&gt;&lt;/sub&gt; &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; y&lt;sub&gt;&lt;font size=2&gt;i+1&lt;/font&gt;&lt;/sub&gt; := aux &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim se &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim para &lt;br&gt;
        fim para &lt;br&gt;
        se (valor &lt; x&lt;sub&gt;&lt;font size=2&gt;0&lt;/font&gt;&lt;/sub&gt;) ou (valor &gt; x&lt;sub&gt;&lt;font size=2&gt;n-1&lt;/font&gt;&lt;/sub&gt;) ) então &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; 'É preciso utilizar um valor dentro do intervalo do conjunto de pontos.' &lt;br&gt;
        fim se &lt;br&gt;
        senão  &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; // executa o método &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; para i de 0 a n-2 faça &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; h&lt;sub&gt;&lt;font size=2&gt;i&lt;/font&gt;&lt;/sub&gt; := x&lt;sub&gt;&lt;font size=2&gt;i+1&lt;/font&gt;&lt;/sub&gt; - x&lt;sub&gt;&lt;font size=2&gt;i&lt;/font&gt;&lt;/sub&gt; &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim para &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; c&lt;sub&gt;&lt;font size=2&gt;1&lt;/font&gt;&lt;/sub&gt; := 2 * (h&lt;sub&gt;&lt;font size=2&gt;0&lt;/font&gt;&lt;/sub&gt; + h&lt;sub&gt;&lt;font size=2&gt;1&lt;/font&gt;&lt;/sub&gt;) &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; para i de 2 a n-2 faça &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; c&lt;sub&gt;&lt;font size=2&gt;i&lt;/font&gt;&lt;/sub&gt; := 2 * (h&lt;sub&gt;&lt;font size=2&gt;i-1&lt;/font&gt;&lt;/sub&gt; + h&lt;sub&gt;&lt;font size=2&gt;i&lt;/font&gt;&lt;/sub&gt;) - ( (h&lt;sub&gt;&lt;font size=2&gt;i-1&lt;/font&gt;&lt;/sub&gt;) * (h&lt;sub&gt;&lt;font size=2&gt;i-1&lt;/font&gt;&lt;/sub&gt;) / c&lt;sub&gt;&lt;font size=2&gt;i-1&lt;/font&gt;&lt;/sub&gt; ) &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim para &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; para i de 0 a n-2 faça &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; b&lt;sub&gt;&lt;font size=2&gt;i&lt;/font&gt;&lt;/sub&gt; := 6 * (y&lt;sub&gt;&lt;font size=2&gt;i+1&lt;/font&gt;&lt;/sub&gt; - y&lt;sub&gt;&lt;font size=2&gt;i&lt;/font&gt;&lt;/sub&gt;) / h&lt;sub&gt;&lt;font size=2&gt;i&lt;/font&gt;&lt;/sub&gt; &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim para &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; d&lt;sub&gt;&lt;font size=2&gt;1&lt;/font&gt;&lt;/sub&gt; = b&lt;sub&gt;&lt;font size=2&gt;1&lt;/font&gt;&lt;/sub&gt; - b&lt;sub&gt;&lt;font size=2&gt;0&lt;/font&gt;&lt;/sub&gt; &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; para i de 2 a n-2 faça &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; d&lt;sub&gt;&lt;font size=2&gt;i&lt;/font&gt;&lt;/sub&gt; := b&lt;sub&gt;&lt;font size=2&gt;i&lt;/font&gt;&lt;/sub&gt; - b&lt;sub&gt;&lt;font size=2&gt;i-1&lt;/font&gt;&lt;/sub&gt; - h&lt;sub&gt;&lt;font size=2&gt;i-1&lt;/font&gt;&lt;/sub&gt; * d&lt;sub&gt;&lt;font size=2&gt;i-1&lt;/font&gt;&lt;/sub&gt; / c&lt;sub&gt;&lt;font size=2&gt;i-1&lt;/font&gt;&lt;/sub&gt; &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim para &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; o&lt;sub&gt;&lt;font size=2&gt;0&lt;/font&gt;&lt;/sub&gt; := 0 &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; o&lt;sub&gt;&lt;font size=2&gt;n-1&lt;/font&gt;&lt;/sub&gt; := 0 &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; o&lt;sub&gt;&lt;font size=2&gt;n-2&lt;/font&gt;&lt;/sub&gt; := d&lt;sub&gt;&lt;font size=2&gt;n-2&lt;/font&gt;&lt;/sub&gt;/c&lt;sub&gt;&lt;font size=2&gt;n-2&lt;/font&gt;&lt;/sub&gt; &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; para i de n-3 a 1 faça &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; o&lt;sub&gt;&lt;font size=2&gt;i&lt;/font&gt;&lt;/sub&gt; := (d&lt;sub&gt;&lt;font size=2&gt;i&lt;/font&gt;&lt;/sub&gt; - h&lt;sub&gt;&lt;font size=2&gt;i&lt;/font&gt;&lt;/sub&gt;* o&lt;sub&gt;&lt;font size=2&gt;i+1&lt;/font&gt;&lt;/sub&gt;) / c&lt;sub&gt;&lt;font size=2&gt;i&lt;/font&gt;&lt;/sub&gt; &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim para &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; // cálculo dos polinômios em cada trecho do conjunto de pontos &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; para i de 0 a n-2 faça &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; alpha&lt;sub&gt;&lt;font size=2&gt;i&lt;/font&gt;&lt;/sub&gt; := ( (y&lt;sub&gt;&lt;font size=2&gt;i+1&lt;/font&gt;&lt;/sub&gt; - y&lt;sub&gt;&lt;font size=2&gt;i&lt;/font&gt;&lt;/sub&gt;) / h&lt;sub&gt;&lt;font size=2&gt;i&lt;/font&gt;&lt;/sub&gt; ) - ( (o&lt;sub&gt;&lt;font size=2&gt;i+1&lt;/font&gt;&lt;/sub&gt; * h&lt;sub&gt;&lt;font size=2&gt;i&lt;/font&gt;&lt;/sub&gt;) / 6 ) - ( (o&lt;sub&gt;&lt;font size=2&gt;i&lt;/font&gt;&lt;/sub&gt; * h&lt;sub&gt;&lt;font size=2&gt;i&lt;/font&gt;&lt;/sub&gt;) / 3 ) &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; beta&lt;sub&gt;&lt;font size=2&gt;i&lt;/font&gt;&lt;/sub&gt; := o&lt;sub&gt;&lt;font size=2&gt;i&lt;/font&gt;&lt;/sub&gt; / 2 &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; gama&lt;sub&gt;&lt;font size=2&gt;i&lt;/font&gt;&lt;/sub&gt; := (o&lt;sub&gt;&lt;font size=2&gt;i+1&lt;/font&gt;&lt;/sub&gt; - o&lt;sub&gt;&lt;font size=2&gt;i&lt;/font&gt;&lt;/sub&gt;) / (6 * h&lt;sub&gt;&lt;font size=2&gt;i&lt;/font&gt;&lt;/sub&gt;) &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim para &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; // interpolação do ponto 'valor' no polinômio i &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; xo := x&lt;sub&gt;&lt;font size=2&gt;0&lt;/font&gt;&lt;/sub&gt; + h&lt;sub&gt;&lt;font size=2&gt;0&lt;/font&gt;&lt;/sub&gt; &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; para j de 0 a n-2 faça &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; i := j &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; se valor &lt;= xo então  &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; j := n + 1 &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim se &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; senão &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; xo := xo + h&lt;sub&gt;&lt;font size=2&gt;j+1&lt;/font&gt;&lt;/sub&gt; &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim senão    &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim para &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; diferenca := valor - x&lt;sub&gt;&lt;font size=2&gt;i&lt;/font&gt;&lt;/sub&gt; &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; solucao = y&lt;sub&gt;&lt;font size=2&gt;i&lt;/font&gt;&lt;/sub&gt; + alpha&lt;sub&gt;&lt;font size=2&gt;i&lt;/font&gt;&lt;/sub&gt; * diferenca + beta&lt;sub&gt;&lt;font size=2&gt;i&lt;/font&gt;&lt;/sub&gt; * diferenca&lt;sup&gt;2&lt;/sup&gt; + gama&lt;sub&gt;&lt;font size=2&gt;i&lt;/font&gt;&lt;/sub&gt; * diferenca&lt;sup&gt;3&lt;/sup&gt; &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; retorna solucao &lt;br&gt;
        fim senão  </traducao>
    <traducao xml:lang="en-us"/>
  </sentenca>
  <sentenca xml:id="SPLINE_AJUDA">
    <traducao xml:lang="pt-br">
        &lt;ul&gt;
        &lt;li&gt;Os arquivos devem estar no formato .txt, e os valores escritos em formato texto.&lt;/li&gt; &lt;br&gt; &lt;br&gt;
        &lt;li&gt;Cada linha deve conter apenas &lt;b&gt;um&lt;/b&gt; valor, na seguinte ordem: &lt;/li&gt; &lt;br&gt; &lt;br&gt;
        &lt;li&gt; &lt;b&gt; Arquivo de dados &lt;/b&gt;
        &lt;br&gt;
        &lt;br&gt; 1ª linha: '0' (Zero) para caso discreto (entrada de dados através de um conjunto de pontos) ou '1' para caso contínuo (entrada de dados através de uma função e um intervalo). &lt;br&gt;
        &lt;br&gt; 2ª linha: Para o caso discreto, '0' (Zero). Para o caso contínuo, '1' se a distribuição dos pontos uniforme ou '2' se a distribuição for de Chebyshev. &lt;br&gt; 
        &lt;br&gt; 3ª linha: número de pontos. &lt;br&gt; 
        &lt;br&gt; Para o caso discreto:
        &lt;ul&gt;
        &lt;li&gt;  &lt;br&gt; A partir da 4ª linha: digitar valores dos pares de pontos x e y, um par em cada linha, da seguinte maneira: x&lt;font size=4&gt;&lt;b&gt;;&lt;/b&gt;&lt;/font&gt;y. &lt;br&gt; &lt;/li&gt;
        &lt;/ul&gt;    
        &lt;br&gt; Para o caso contínuo:
        &lt;ul&gt;
        &lt;li&gt; &lt;br&gt; 4ª linha: função do problema, no &lt;a href=javascript:winopen('funcoesphp.php')&gt;formato&lt;/a&gt; reconhecido pelo programa. &lt;br&gt; &lt;/li&gt;
        &lt;li&gt; &lt;br&gt; 5ª linha: intervalo a,b da função, escrito na forma: a&lt;font size=4&gt;&lt;b&gt;;&lt;/b&gt;&lt;/font&gt;b. &lt;br&gt; &lt;/li&gt;
        &lt;/ul&gt;    
        &lt;br&gt; 
        &lt;br&gt; Última linha: valor a ser interpolado. &lt;br&gt; &lt;br&gt;
        &lt;li&gt; &lt;b&gt; Arquivo de resposta &lt;/b&gt;
        &lt;br&gt;
        &lt;br&gt; 1ª linha: trecho que gerou o polinômio. &lt;br&gt;
        &lt;br&gt; 2ª linha: intervalo a,b que gerou o polinômio, escrito na forma: a&lt;font size=4&gt;&lt;font size=4&gt;&lt;b&gt;;&lt;/b&gt;&lt;/font&gt;&lt;/font&gt;b. &lt;br&gt;
        &lt;br&gt; A partir da 3ª linha: coeficientes do polinômio interpolador. &lt;br&gt;
        &lt;br&gt; Formato do polinômio: 
        &lt;br&gt; p&lt;sub&gt;trecho&lt;/sub&gt;(x) = coef&lt;sub&gt;1&lt;/sub&gt; + coef&lt;sub&gt;2&lt;/sub&gt; (x - coef&lt;sub&gt;3&lt;/sub&gt;) + coef&lt;sub&gt;4&lt;/sub&gt; (x - coef&lt;sub&gt;5&lt;/sub&gt;)&lt;sup&gt;2&lt;/sup&gt; + coef&lt;sub&gt;6&lt;/sub&gt; (x - coef&lt;sub&gt;7&lt;/sub&gt;)&lt;sup&gt;3&lt;/sup&gt; &lt;br&gt;
        &lt;br&gt; Última linha: valor interpolado.
        &lt;/ul&gt;
    </traducao>
    <traducao xml:lang="en-us"/>
  </sentenca>
  <sentenca xml:id="TRANSPOSTA_MSG_01">
    <traducao xml:lang="pt-br">Transposição de Matrizes</traducao>
    <traducao xml:lang="en-us">Transposing Matrices</traducao>
  </sentenca>
  <sentenca xml:id="TRANSPOSTA_MSG_02">
    <traducao xml:lang="pt-br">Aritmética Matricial</traducao>
    <traducao xml:lang="en-us">Matricial Arithmetic</traducao>
  </sentenca>
  <sentenca xml:id="TRANSPOSTA_MSG_03">
    <traducao xml:lang="pt-br">Transposta</traducao>
    <traducao xml:lang="en-us">Transpose</traducao>
  </sentenca>
  <sentenca xml:id="TRANSPOSTA_MSG_04">
    <traducao xml:lang="pt-br">Dimensão: </traducao>
    <traducao xml:lang="en-us">Dimension: </traducao>
  </sentenca>
  <sentenca xml:id="TRANSPOSTA_MSG_05">
    <traducao xml:lang="pt-br">Matriz A</traducao>
    <traducao xml:lang="en-us">Matrix A</traducao>
  </sentenca>
  <sentenca xml:id="TRANSPOSTA_MSG_06">
    <traducao xml:lang="pt-br">Matriz B (A&lt;sup&gt;t&lt;/sup&gt;) - Resposta obtida do arquivo:</traducao>
    <traducao xml:lang="en-us">Matrix B (A&lt;sup&gt;t&lt;/sup&gt;) - Gotten answer of the archive:</traducao>
  </sentenca>
  <sentenca xml:id="TRANSPOSTA_MSG_07">
    <traducao xml:lang="pt-br">Matriz B (A&lt;sup&gt;t&lt;/sup&gt;) - Resposta obtida do programa: </traducao>
    <traducao xml:lang="en-us">Matrix B (A&lt;sup&gt;t&lt;/sup&gt;) - Gotten answer of the program: </traducao>
  </sentenca>
  <sentenca xml:id="TRANSPOSTA_ALGORITMO">
    <traducao xml:lang="pt-br">
        &lt;b&gt;Variáveis: &lt;/b&gt; &lt;br&gt;&lt;br&gt; 
        Auxiliares: &lt;br&gt;
        i, j (contadores) &lt;br&gt;&lt;br&gt;
        De entrada: &lt;br&gt;
        A (matriz), dim (dimensão da matriz) &lt;br&gt;&lt;br&gt;
        De saída: &lt;br&gt;
        B (matriz)&lt;br&gt;&lt;br&gt;
        &lt;b&gt;Algoritmo: &lt;/b&gt; &lt;br&gt;&lt;br&gt; 
        para i de 0 a dim-1 faça &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; para j de 0 a dim-1 faça &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; B&lt;sub&gt;&lt;font size=2&gt;i,j&lt;/font&gt;&lt;/sub&gt; := A&lt;sub&gt;&lt;font size=2&gt;j,i&lt;/font&gt;&lt;/sub&gt; &lt;br&gt;
        &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; fim para j &lt;br&gt;
        fim para i &lt;br&gt;
        retorna B </traducao>
    <traducao xml:lang="en-us"/>
  </sentenca>
  <sentenca xml:id="TRANSPOSTA_AJUDA">
    <traducao xml:lang="pt-br">
        &lt;ul&gt;
        &lt;li&gt;Os arquivos devem estar no formato .txt&lt;/li&gt; &lt;br&gt;
        &lt;li&gt;Cada linha deve conter apenas &lt;b&gt;um&lt;/b&gt; elemento, na seguinte ordem: &lt;/li&gt; &lt;br&gt; 
        &lt;li&gt; &lt;b&gt; Arquivo de dados &lt;/b&gt;
        &lt;br&gt;
        &lt;br&gt; 1ª linha: número de linhas da matriz. &lt;br&gt;
        &lt;br&gt; 2ª linha: número de colunas da matriz. &lt;br&gt;
        &lt;br&gt; Em seguida: valores da matriz A (um por linha), em ordem crescente de coluna e linha. &lt;br&gt;
        &lt;br&gt;
        &lt;li&gt; &lt;b&gt; Arquivo de resposta &lt;/b&gt;
        &lt;br&gt;
        &lt;br&gt; A partir da 1ª linha: elementos da matriz B, em ordem crescente de coluna e linha. &lt;br&gt;
        &lt;/ul&gt;
    </traducao>
    <traducao xml:lang="en-us"/>
  </sentenca>
  <sentenca xml:id="XML_NEXT">
    <traducao xml:lang="pt-br">'Próximo &gt;&gt;'</traducao>
    <traducao xml:lang="en-us">'Next >>'</traducao>
  </sentenca>
  <sentenca xml:id="XML_BEGIN">
    <traducao xml:lang="pt-br">'&gt;&gt;Início&lt;&lt;'</traducao>
    <traducao xml:lang="en-us">'&gt;&gt;Beginning&lt;&lt;'</traducao>
  </sentenca>
  <sentenca xml:id="XML_BACK">
    <traducao xml:lang="pt-br">'&lt;&lt; Voltar'</traducao>
    <traducao xml:lang="en-us">'&lt;&lt; Go Back'</traducao>
  </sentenca>
  <sentenca xml:id="XML_TITLE">
    <traducao xml:lang="pt-br">Biblioteca de Problemas Matemáticos Integrada  à Execução de Algoritmos Via Web</traducao>
    <traducao xml:lang="en-us">Library of Mathematical Problems Integrated into the Execution of Algorithms through Web</traducao>
  </sentenca>
  <sentenca xml:id="XML_TITLE_GERA">
    <traducao xml:lang="pt-br">AUTORIA DE EXEMPLOS</traducao>
    <traducao xml:lang="en-us">Examples Generation</traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_MSG01">
    <traducao xml:lang="pt-br">Opções para autoria de exemplo: </traducao>
    <traducao xml:lang="en-us">Select an option to input data: </traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_MSG02">
    <traducao xml:lang="pt-br">Criar problema através do teclado</traducao>
    <traducao xml:lang="en-us">Through keyboard</traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_MSG03">
    <traducao xml:lang="pt-br">Criar problema através de um arquivo em formato texto</traducao>
    <traducao xml:lang="en-us">Through plain-text file</traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_MSG04">
    <traducao xml:lang="pt-br">Localização do arquivo de dados: </traducao>
    <traducao xml:lang="en-us">Data file location: </traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_MSG05">
    <traducao xml:lang="pt-br">Formato do arquivo de dados</traducao>
    <traducao xml:lang="en-us">Data file format</traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_MSG06">
    <traducao xml:lang="pt-br">Caminho ou arquivo inexistente...</traducao>
    <traducao xml:lang="en-us">Path or file not found...</traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_MSG07">
    <traducao xml:lang="pt-br">Descrição do Sistema: </traducao>
    <traducao xml:lang="en-us">System Description: </traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_MSG08">
    <traducao xml:lang="pt-br">Comentários (opcional): </traducao>
    <traducao xml:lang="en-us">Comments (optional): </traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_MSG09">
    <traducao xml:lang="pt-br">Referência Bibliográfica (opcional): </traducao>
    <traducao xml:lang="en-us">References (optional): </traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_MSG010">
    <traducao xml:lang="pt-br">Gerar Exemplo</traducao>
    <traducao xml:lang="en-us">Generate Example</traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_MSG011">
    <traducao xml:lang="pt-br">Exemplo gerado com sucesso!</traducao>
    <traducao xml:lang="en-us">Example generated successfully!</traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_MSG12">
    <traducao xml:lang="pt-br">Alterar um problema</traducao>
    <traducao xml:lang="en-us">Change a problem</traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_MSG13">
    <traducao xml:lang="pt-br">Remover um problema</traducao>
    <traducao xml:lang="en-us">Remove a problem</traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_MSG14">
    <traducao xml:lang="pt-br">Alterar exemplo</traducao>
    <traducao xml:lang="en-us">Change example</traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_MSG15">
    <traducao xml:lang="pt-br">Remover exemplo</traducao>
    <traducao xml:lang="en-us">Remove example</traducao>
  </sentenca>
  <sentenca xml:id="XML_EXIBE_MSG01">
    <traducao xml:lang="pt-br">Deseja visualizar exemplos de qual professor (a) ?</traducao>
    <traducao xml:lang="en-us">Which teacher would you like to view examples from?</traducao>
  </sentenca>
  <sentenca xml:id="XML_EXIBE_MSG02">
    <traducao xml:lang="pt-br">Biblioteca Demo</traducao>
    <traducao xml:lang="en-us">Demo Library</traducao>
  </sentenca>
  <sentenca xml:id="XML_EXIBE_MSG03">
    <traducao xml:lang="pt-br">Enviar</traducao>
    <traducao xml:lang="en-us">Send</traducao>
  </sentenca>
  <sentenca xml:id="XML_EXIBE_MSG04">
    <traducao xml:lang="pt-br">Clique em um dos links abaixo para visualizar o exemplo :</traducao>
    <traducao xml:lang="en-us">Click on the links below to view the examples: </traducao>
  </sentenca>
  <sentenca xml:id="XML_EXIBE_MSG05">
    <traducao xml:lang="pt-br">Não constam exemplos referentes a este método, cadastrados na biblioteca de problemas!</traducao>
    <traducao xml:lang="en-us">There is no example related to this method stored in this library!</traducao>
  </sentenca>
  <sentenca xml:id="XML_EXIBE_MSG06">
    <traducao xml:lang="pt-br">Não foi encontrado nenhuma biblioteca de problemas exemplos referente ao professor escolhido!</traducao>
    <traducao xml:lang="en-us">No library of example problems was found related to the teacher chosen!</traducao>
  </sentenca>
  <sentenca xml:id="XML_EXIBE_MSG07">
    <traducao xml:lang="pt-br">'Visualizar exemplos de outro professor'</traducao>
    <traducao xml:lang="en-us">'View examples from another teacher'</traducao>
  </sentenca>
  <sentenca xml:id="XML_EXIBE_MSG08">
    <traducao xml:lang="pt-br">Comentário:</traducao>
    <traducao xml:lang="en-us">Comment:</traducao>
  </sentenca>
  <sentenca xml:id="XML_EXIBE_MSG09">
    <traducao xml:lang="pt-br">Referência:</traducao>
    <traducao xml:lang="en-us">Reference:</traducao>
  </sentenca>
  <sentenca xml:id="XML_EXIBE_MSG010">
    <traducao xml:lang="pt-br">Calcular</traducao>
    <traducao xml:lang="en-us">Calculate</traducao>
  </sentenca>
  <sentenca xml:id="XML_EXIBE_MSG011">
    <traducao xml:lang="pt-br">'Voltar ao menu de exemplos'</traducao>
    <traducao xml:lang="en-us">'Back to examples menu'</traducao>
  </sentenca>
  <sentenca xml:id="XML_TITLE_SELA">
    <traducao xml:lang="pt-br">Sistemas de Equações Algébricas Lineares</traducao>
    <traducao xml:lang="en-us">System of Linear Algebraic Equations</traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_SELA_SUBTITLE_1">
    <traducao xml:lang="pt-br">Eliminação de Gauss - Sem pivoteamento</traducao>
    <traducao xml:lang="en-us">Gauss Elimination - Without pivoting</traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_SELA_SUBTITLE_2">
    <traducao xml:lang="pt-br">Eliminação de Gauss - Com pivoteamento parcial</traducao>
    <traducao xml:lang="en-us">Gauss Elimination - With partial pivoting</traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_SELA_SUBTITLE_3">
    <traducao xml:lang="pt-br">Eliminação de Gauss - Com pivoteamento parcial</traducao>
    <traducao xml:lang="en-us">Gauss Elimination - With total pivoting</traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_SELA_SUBTITLE_4">
    <traducao xml:lang="pt-br">Decomposição LU</traducao>
    <traducao xml:lang="en-us">LU Decomposition</traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_SELA_SUBTITLE_5">
    <traducao xml:lang="pt-br">Cholesky</traducao>
    <traducao xml:lang="en-us">Cholesky</traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_SELA_SUBTITLE_6">
    <traducao xml:lang="pt-br">Gauss-Seidel</traducao>
    <traducao xml:lang="en-us">Gauss-Seidel</traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_SELA_SUBTITLE_7">
    <traducao xml:lang="pt-br">Jacobi</traducao>
    <traducao xml:lang="en-us">Jacobi</traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_SELA_MSG01">
    <traducao xml:lang="pt-br">Número de variáveis:</traducao>
    <traducao xml:lang="en-us">Number of variables:</traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_SELA_MSG02">
    <traducao xml:lang="pt-br">Sistema: </traducao>
    <traducao xml:lang="en-us">System: </traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_SELA_MSG03">
    <traducao xml:lang="pt-br">Propriedades do Sistema: </traducao>
    <traducao xml:lang="en-us">System Properties: </traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_SELA_MSG04">
    <traducao xml:lang="pt-br">Verificar</traducao>
    <traducao xml:lang="en-us">Verify</traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_SELA_MSG05">
    <traducao xml:lang="pt-br">Tipo de Solução</traducao>
    <traducao xml:lang="en-us">Type of Solution</traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_SELA_MSG06">
    <traducao xml:lang="pt-br">Compatível Determinado</traducao>
    <traducao xml:lang="en-us">Determined Compatible</traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_SELA_MSG07">
    <traducao xml:lang="pt-br">Compatível Indeterminado</traducao>
    <traducao xml:lang="en-us">Undetermined Compatible</traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_SELA_MSG08">
    <traducao xml:lang="pt-br">Incompatível</traducao>
    <traducao xml:lang="en-us">Incompatible</traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_SELA_MSG09">
    <traducao xml:lang="pt-br">Sim</traducao>
    <traducao xml:lang="en-us">Yes</traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_SELA_MSG010">
    <traducao xml:lang="pt-br">Não</traducao>
    <traducao xml:lang="en-us">No</traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_SELA_MSG011">
    <traducao xml:lang="pt-br">Simétrico: </traducao>
    <traducao xml:lang="en-us">Symetric: </traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_SELA_MSG012">
    <traducao xml:lang="pt-br">Esparso: </traducao>
    <traducao xml:lang="en-us">Sparse: </traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_SELA_MSG013">
    <traducao xml:lang="pt-br">Definido Positivo:</traducao>
    <traducao xml:lang="en-us">Definite Positive</traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_SELA_MSG014">
    <traducao xml:lang="pt-br">Diagonalmente Dominante:</traducao>
    <traducao xml:lang="en-us">Diagonally Dominant:</traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_SELA_MSG015">
    <traducao xml:lang="pt-br">Número máximo de iterações:</traducao>
    <traducao xml:lang="en-us">Maximum Number of Iterations:</traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_SELA_MSG016">
    <traducao xml:lang="pt-br">&gt;k&lt;/sup&gt;&lt;/font&gt;&amp;nbsp):</traducao>
    <traducao xml:lang="en-us">Minimum Precision Required (enter the k value to 10&lt;sup&gt;-&lt;font size="2"&gt;k&lt;/sup&gt;&lt;/font&gt;&amp;nbsp):</traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_SELA_MSG017">
    <traducao xml:lang="pt-br">Precisão desejada:</traducao>
    <traducao xml:lang="en-us">Minimum Precision Required:</traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_SELA_MSG018">
    <traducao xml:lang="pt-br">Sistema</traducao>
    <traducao xml:lang="en-us">System</traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_SELA_MSG019">
    <traducao xml:lang="pt-br">Aproximações de X</traducao>
    <traducao xml:lang="en-us">X-Approximations</traducao>
  </sentenca>
  <sentenca xml:id="XML_EXIBE_SELA_SUBTITLE_1">
    <traducao xml:lang="pt-br">Eliminação de Gauss - Sem pivoteamento</traducao>
    <traducao xml:lang="en-us">Gauss Elimination - Without pivoting</traducao>
  </sentenca>
  <sentenca xml:id="XML_EXIBE_SELA_SUBTITLE_2">
    <traducao xml:lang="pt-br">Eliminação de Gauss - Com pivoteamento parcial</traducao>
    <traducao xml:lang="en-us">Gauss Elimination - With partial pivoting</traducao>
  </sentenca>
  <sentenca xml:id="XML_EXIBE_SELA_SUBTITLE_3">
    <traducao xml:lang="pt-br">Eliminação de Gauss - Com pivoteamento parcial</traducao>
    <traducao xml:lang="en-us">Gauss Elimination - With total pivoting</traducao>
  </sentenca>
  <sentenca xml:id="XML_EXIBE_SELA_SUBTITLE_4">
    <traducao xml:lang="pt-br">Decomposição LU</traducao>
    <traducao xml:lang="en-us">LU Decomposition</traducao>
  </sentenca>
  <sentenca xml:id="XML_EXIBE_SELA_SUBTITLE_5">
    <traducao xml:lang="pt-br">Cholesky</traducao>
    <traducao xml:lang="en-us">Cholesky</traducao>
  </sentenca>
  <sentenca xml:id="XML_EXIBE_SELA_SUBTITLE_6">
    <traducao xml:lang="pt-br">Gauss-Seidel</traducao>
    <traducao xml:lang="en-us">Gauss-Seidl</traducao>
  </sentenca>
  <sentenca xml:id="XML_EXIBE_SELA_SUBTITLE_7">
    <traducao xml:lang="pt-br">Jacobi</traducao>
    <traducao xml:lang="en-us">Jacobi</traducao>
  </sentenca>
  <sentenca xml:id="XML_EXIBE_SELA_MSG01">
    <traducao xml:lang="pt-br">Sistema de dimensão </traducao>
    <traducao xml:lang="en-us">System of Dimension </traducao>
  </sentenca>
  <sentenca xml:id="XML_EXIBE_SELA_MSG02">
    <traducao xml:lang="pt-br">Número de variáveis:</traducao>
    <traducao xml:lang="en-us">Number of variables:</traducao>
  </sentenca>
  <sentenca xml:id="XML_EXIBE_SELA_MSG03">
    <traducao xml:lang="pt-br">Descrição:</traducao>
    <traducao xml:lang="en-us">Description:</traducao>
  </sentenca>
  <sentenca xml:id="XML_EXIBE_SELA_MSG04">
    <traducao xml:lang="pt-br">Sistema:</traducao>
    <traducao xml:lang="en-us">System:</traducao>
  </sentenca>
  <sentenca xml:id="XML_EXIBE_SELA_MSG05">
    <traducao xml:lang="pt-br">Número máximo de iterações:</traducao>
    <traducao xml:lang="en-us">Maximum Number of Iterations:</traducao>
  </sentenca>
  <sentenca xml:id="XML_EXIBE_SELA_MSG06">
    <traducao xml:lang="pt-br">Precisão desejada :</traducao>
    <traducao xml:lang="en-us">Minimum Precision Required:</traducao>
  </sentenca>
  <sentenca xml:id="XML_EXIBE_SELA_MSG07">
    <traducao xml:lang="pt-br">Aproximações de X</traducao>
    <traducao xml:lang="en-us">X-Approximations</traducao>
  </sentenca>
  <sentenca xml:id="XML_TITLE_MATRIZ">
    <traducao xml:lang="pt-br">Aritmética Matricial</traducao>
    <traducao xml:lang="en-us">Matricial Arithmetic</traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_MATRIZ_SUBTITLE_1">
    <traducao xml:lang="pt-br">Matrizes definidas positivas</traducao>
    <traducao xml:lang="en-us">Positive-Definite</traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_MATRIZ_SUBTITLE_2">
    <traducao xml:lang="pt-br">Determinante</traducao>
    <traducao xml:lang="en-us">Determinant</traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_MATRIZ_SUBTITLE_3">
    <traducao xml:lang="pt-br">Inversa</traducao>
    <traducao xml:lang="en-us">Inverse</traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_MATRIZ_SUBTITLE_4">
    <traducao xml:lang="pt-br">Multiplicação</traducao>
    <traducao xml:lang="en-us">Multiplication</traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_MATRIZ_SUBTITLE_5">
    <traducao xml:lang="pt-br">Soma</traducao>
    <traducao xml:lang="en-us">Addition</traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_MATRIZ_SUBTITLE_6">
    <traducao xml:lang="pt-br">Transposta</traducao>
    <traducao xml:lang="en-us">Transposition</traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_MATRIZ_SUBTITLE_7">
    <traducao xml:lang="pt-br">Decomposição de matrizes</traducao>
    <traducao xml:lang="en-us">Decomposition of matrices</traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_MATRIZ_MSG01">
    <traducao xml:lang="pt-br">Dimensão:</traducao>
    <traducao xml:lang="en-us">Dimension:</traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_MATRIZ_MSG02">
    <traducao xml:lang="pt-br">Matriz A:</traducao>
    <traducao xml:lang="en-us">Matrix A:</traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_MATRIZ_MSG03">
    <traducao xml:lang="pt-br">Descrição da Matriz:</traducao>
    <traducao xml:lang="en-us">Matrix Description:</traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_MATRIZ_MSG05">
    <traducao xml:lang="pt-br">Dimensão da Matriz A:</traducao>
    <traducao xml:lang="en-us">Dimension of Matrix A:</traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_MATRIZ_MSG06">
    <traducao xml:lang="pt-br">Dimensão Inválida! Número de colunas de A deve ser igual ao número de linhas de B.</traducao>
    <traducao xml:lang="en-us">Invalid Dimension! The number of columns of matrix A must match the number of rows of matrix B.</traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_MATRIZ_MSG07">
    <traducao xml:lang="pt-br">Dimensão da Matriz B:</traducao>
    <traducao xml:lang="en-us">Dimension of Matrix B:</traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_MATRIZ_MSG08">
    <traducao xml:lang="pt-br">Matriz B </traducao>
    <traducao xml:lang="en-us">Matrix B</traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_MATRIZ_MSG09">
    <traducao xml:lang="pt-br">Descrição das Matrizes:</traducao>
    <traducao xml:lang="en-us">Matrices Description:</traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_MATRIZ_MSG010">
    <traducao xml:lang="pt-br">Dimensão das Matrizes:</traducao>
    <traducao xml:lang="en-us">Matrices Dimension:</traducao>
  </sentenca>
  <sentenca xml:id="XML_EXIBE_MATRIZ_SUBTITLE_1">
    <traducao xml:lang="pt-br">Matrizes definidas positivas</traducao>
    <traducao xml:lang="en-us">Positive-Definite</traducao>
  </sentenca>
  <sentenca xml:id="XML_EXIBE_MATRIZ_SUBTITLE_2">
    <traducao xml:lang="pt-br">Determinante</traducao>
    <traducao xml:lang="en-us">Determinant</traducao>
  </sentenca>
  <sentenca xml:id="XML_EXIBE_MATRIZ_SUBTITLE_3">
    <traducao xml:lang="pt-br">Inversa</traducao>
    <traducao xml:lang="en-us">Inverse</traducao>
  </sentenca>
  <sentenca xml:id="XML_EXIBE_MATRIZ_SUBTITLE_4">
    <traducao xml:lang="pt-br">Multiplicação</traducao>
    <traducao xml:lang="en-us">Multiplication</traducao>
  </sentenca>
  <sentenca xml:id="XML_EXIBE_MATRIZ_SUBTITLE_5">
    <traducao xml:lang="pt-br">Soma</traducao>
    <traducao xml:lang="en-us">Addition</traducao>
  </sentenca>
  <sentenca xml:id="XML_EXIBE_MATRIZ_SUBTITLE_6">
    <traducao xml:lang="pt-br">Transposta</traducao>
    <traducao xml:lang="en-us">Transposition</traducao>
  </sentenca>
  <sentenca xml:id="XML_EXIBE_MATRIZ_SUBTITLE_7">
    <traducao xml:lang="pt-br">Decomposição de matrizes</traducao>
    <traducao xml:lang="en-us">Decomposition of matrices</traducao>
  </sentenca>
  <sentenca xml:id="XML_EXIBE_MATRIZ_MSG01">
    <traducao xml:lang="pt-br">Matriz de dimensão </traducao>
    <traducao xml:lang="en-us">Matrix of Dimension </traducao>
  </sentenca>
  <sentenca xml:id="XML_EXIBE_MATRIZ_MSG02">
    <traducao xml:lang="pt-br">Dimensão:</traducao>
    <traducao xml:lang="en-us">Dimension:</traducao>
  </sentenca>
  <sentenca xml:id="XML_EXIBE_MATRIZ_MSG03">
    <traducao xml:lang="pt-br">Descrição:</traducao>
    <traducao xml:lang="en-us">Description:</traducao>
  </sentenca>
  <sentenca xml:id="XML_EXIBE_MATRIZ_MSG04">
    <traducao xml:lang="pt-br">Matriz:</traducao>
    <traducao xml:lang="en-us">Matrix:</traducao>
  </sentenca>
  <sentenca xml:id="XML_EXIBE_MATRIZ_MSG05">
    <traducao xml:lang="pt-br">Determinante de dimensão </traducao>
    <traducao xml:lang="en-us">Determinant of dimension </traducao>
  </sentenca>
  <sentenca xml:id="XML_EXIBE_MATRIZ_MSG06">
    <traducao xml:lang="pt-br">Matrizes de dimensões </traducao>
    <traducao xml:lang="en-us">Matrices of dimensions </traducao>
  </sentenca>
  <sentenca xml:id="XML_EXIBE_MATRIZ_MSG07">
    <traducao xml:lang="pt-br">Matrizes:</traducao>
    <traducao xml:lang="en-us">Matrices:</traducao>
  </sentenca>
  <sentenca xml:id="XML_TITLE_PTOFLU">
    <traducao xml:lang="pt-br">Aritmética de Ponto Flutuante</traducao>
    <traducao xml:lang="en-us">Floating Point Arithmetic</traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_PTOFLU_SUBTITLE_1">
    <traducao xml:lang="pt-br">Divisão</traducao>
    <traducao xml:lang="en-us">Division</traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_PTOFLU_SUBTITLE_2">
    <traducao xml:lang="pt-br">Multiplicação</traducao>
    <traducao xml:lang="en-us">Multiplication</traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_PTOFLU_SUBTITLE_3">
    <traducao xml:lang="pt-br">Sistema de Ponto Flutuante</traducao>
    <traducao xml:lang="en-us">Floating Point System</traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_PTOFLU_SUBTITLE_4">
    <traducao xml:lang="pt-br">Soma</traducao>
    <traducao xml:lang="en-us">Addition</traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_PTOFLU_SUBTITLE_5">
    <traducao xml:lang="pt-br">Subtração</traducao>
    <traducao xml:lang="en-us">Subtraction</traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_PTOFLU_MSG01">
    <traducao xml:lang="pt-br">Geração de dados para dividir dois números em ponto flutuante, a partir de um dado sistema de ponto flutuante F(b,m,e&lt;sub&gt;inf&lt;/sub&gt;,
        e&lt;sub&gt;sup&lt;/sub&gt;), onde b=base, m=mantissa, e&lt;sub&gt;inf&lt;/sub&gt;=expoente inferior e e&lt;sub&gt;sup&lt;/sub&gt;=expoente superior.</traducao>
    <traducao xml:lang="en-us">Data generation to divide two numbers in floating point, from a given floating point system F(b,m,e&lt;sub&gt;1&lt;/sub&gt;,
        e&lt;sub&gt;2&lt;/sub&gt;), where b=base, m=mantissa, e&lt;sub&gt;1&lt;/sub&gt;=minimum exponent and e&lt;sub&gt;2&lt;/sub&gt;=maximum exponent.</traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_PTOFLU_MSG02">
    <traducao xml:lang="pt-br">Geração de dados para multiplicar dois números em ponto flutuante, a partir de um dado sistema de ponto flutuante F(b,m,e&lt;sub&gt;inf&lt;/sub&gt;,
        e&lt;sub&gt;sup&lt;/sub&gt;), onde b=base, m=mantissa, e&lt;sub&gt;inf&lt;/sub&gt;=expoente inferior e e&lt;sub&gt;sup&lt;/sub&gt;=expoente superior.</traducao>
    <traducao xml:lang="en-us">Data generation to multiply two numbers in floating point, from a given floating point system F(b,m,e&lt;sub&gt;1&lt;/sub&gt;,
        e&lt;sub&gt;2&lt;/sub&gt;), where b=base, m=mantissa, e&lt;sub&gt;1&lt;/sub&gt;=minimum exponent and e&lt;sub&gt;2&lt;/sub&gt;=maximum exponent.</traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_PTOFLU_MSG03">
    <traducao xml:lang="pt-br">Geração de dados de um sistema de ponto flutuante F(b,m,e&lt;sub&gt;inf&lt;/sub&gt;,e&lt;sub&gt;sup&lt;/sub&gt;),
        onde b=base, m=mantissa, e&lt;sub&gt;inf&lt;/sub&gt;=expoente inferior e e&lt;sub&gt;sup&lt;/sub&gt;=expoente superior.</traducao>
    <traducao xml:lang="en-us">Data generation from a floating point system F(b,m,e&lt;sub&gt;1&lt;/sub&gt;,e&lt;sub&gt;2&lt;/sub&gt;),
        where b=base, m=mantissa, e&lt;sub&gt;1&lt;/sub&gt;=minimum exponent and e&lt;sub&gt;2&lt;/sub&gt;=maximum exponent.</traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_PTOFLU_MSG04">
    <traducao xml:lang="pt-br">Geração de dados para somar dois números em ponto flutuante, a partir de um dado sistema de ponto flutuante
        F(b,m,e&lt;sub&gt;inf&lt;/sub&gt;,e&lt;sub&gt;sup&lt;/sub&gt;), onde b=base, m=mantissa, e&lt;sub&gt;inf&lt;/sub&gt;=expoente inferior e e&lt;sub&gt;sup&lt;/sub&gt;=expoente superior.</traducao>
    <traducao xml:lang="en-us">Data generation to add two numbers in floating point, from a given floating point system
        F(b,m,e&lt;sub&gt;1&lt;/sub&gt;,e&lt;sub&gt;2&lt;/sub&gt;), where b=base, m=mantissa, e&lt;sub&gt;1&lt;/sub&gt;=minimum exponent and e&lt;sub&gt;2&lt;/sub&gt;=maximum exponent.</traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_PTOFLU_MSG05">
    <traducao xml:lang="pt-br">Geração de dados para subtrair dois números em ponto flutuante, a partir de um dado sistema de ponto flutuante
        F(b,m,e&lt;sub&gt;inf&lt;/sub&gt;,e&lt;sub&gt;sup&lt;/sub&gt;), onde b=base, m=mantissa, e&lt;sub&gt;inf&lt;/sub&gt;=expoente inferior e e&lt;sub&gt;sup&lt;/sub&gt;=expoente superior.</traducao>
    <traducao xml:lang="en-us">Data generation to subtract two numbers in floating point, from a given floating point system
        F(b,m,e&lt;sub&gt;1&lt;/sub&gt;,e&lt;sub&gt;2&lt;/sub&gt;), where b=base, m=mantissa, e&lt;sub&gt;1&lt;/sub&gt;=minimum exponent and e&lt;sub&gt;2&lt;/sub&gt;=maximum exponent.</traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_PTOFLU_MSG06">
    <traducao xml:lang="pt-br">Entrada de dados:</traducao>
    <traducao xml:lang="en-us">Data input:</traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_PTOFLU_MSG07">
    <traducao xml:lang="pt-br">em decimal</traducao>
    <traducao xml:lang="en-us">in decimal</traducao>
  </sentenca>
  <sentenca xml:id="XML_EXIBE_PTOFLU_SUBTITLE_1">
    <traducao xml:lang="pt-br">Divisão</traducao>
    <traducao xml:lang="en-us">Division</traducao>
  </sentenca>
  <sentenca xml:id="XML_EXIBE_PTOFLU_SUBTITLE_2">
    <traducao xml:lang="pt-br">Multiplicação</traducao>
    <traducao xml:lang="en-us">Multiplication</traducao>
  </sentenca>
  <sentenca xml:id="XML_EXIBE_PTOFLU_SUBTITLE_3">
    <traducao xml:lang="pt-br">Sistema de Ponto Flutuante</traducao>
    <traducao xml:lang="en-us">Floating Point System</traducao>
  </sentenca>
  <sentenca xml:id="XML_EXIBE_PTOFLU_SUBTITLE_4">
    <traducao xml:lang="pt-br">Soma</traducao>
    <traducao xml:lang="en-us">Addition</traducao>
  </sentenca>
  <sentenca xml:id="XML_EXIBE_PTOFLU_SUBTITLE_5">
    <traducao xml:lang="pt-br">Subtração</traducao>
    <traducao xml:lang="en-us">Subtraction</traducao>
  </sentenca>
  <sentenca xml:id="XML_EXIBE_PTOFLU_MSG01">
    <traducao xml:lang="pt-br">Exemplo</traducao>
    <traducao xml:lang="en-us">Example</traducao>
  </sentenca>
  <sentenca xml:id="XML_EXIBE_PTOFLU_MSG02">
    <traducao xml:lang="pt-br">Descrição:</traducao>
    <traducao xml:lang="en-us">Description:</traducao>
  </sentenca>
  <sentenca xml:id="XML_EXIBE_PTOFLU_MSG03">
    <traducao xml:lang="pt-br">Dados para dividir dois números em ponto flutuante, a partir de um dado sistema de ponto flutuante
        F(b,m,e&lt;sub&gt;inf&lt;/sub&gt;,e&lt;sub&gt;sup&lt;/sub&gt;), onde b=base, m=mantissa, e&lt;sub&gt;inf&lt;/sub&gt;=expoente inferior e e&lt;sub&gt;sup&lt;/sub&gt;=expoente superior.</traducao>
    <traducao xml:lang="en-us">Data to divide two numbers in floating point, from a given floating point system F(b,m,e&lt;sub&gt;1&lt;/sub&gt;,e&lt;sub&gt;2&lt;/sub&gt;), where b=base, m=mantissa, e&lt;sub&gt;1&lt;/sub&gt;=minimum exponent and e&lt;sub&gt;2&lt;/sub&gt;=maximum exponent.</traducao>
  </sentenca>
  <sentenca xml:id="XML_EXIBE_PTOFLU_MSG04">
    <traducao xml:lang="pt-br">em decimal</traducao>
    <traducao xml:lang="en-us">in decimal</traducao>
  </sentenca>
  <sentenca xml:id="XML_EXIBE_PTOFLU_MSG05">
    <traducao xml:lang="pt-br">Dados para multiplicar dois números em ponto flutuante, a partir de um dado sistema de ponto flutuante
        F(b,m,e&lt;sub&gt;inf&lt;/sub&gt;,e&lt;sub&gt;sup&lt;/sub&gt;), onde b=base, m=mantissa, e&lt;sub&gt;inf&lt;/sub&gt;=expoente inferior e e&lt;sub&gt;sup&lt;/sub&gt;=expoente superior.</traducao>
    <traducao xml:lang="en-us">Data to multiply two numbers in floating point, from a given floating point system
        F(b,m,e&lt;sub&gt;1&lt;/sub&gt;,e&lt;sub&gt;2&lt;/sub&gt;), where b=base, m=mantissa, e&lt;sub&gt;1&lt;/sub&gt;=minimum exponent and e&lt;sub&gt;2&lt;/sub&gt;=maximum exponent.</traducao>
  </sentenca>
  <sentenca xml:id="XML_EXIBE_PTOFLU_MSG06">
    <traducao xml:lang="pt-br">Dados para gerar o conjunto de todos os números em ponto flutuante, a partir de um dado sistema de ponto flutuante
        F(b,m,e&lt;sub&gt;inf&lt;/sub&gt;,e&lt;sub&gt;sup&lt;/sub&gt;), onde b=base, m=mantissa, e&lt;sub&gt;inf&lt;/sub&gt;=expoente inferior e e&lt;sub&gt;sup&lt;/sub&gt;=expoente superior.</traducao>
    <traducao xml:lang="en-us">Data to generate the set of all numbers in floating point, from a given floating point system
        F(b,m,e&lt;sub&gt;1&lt;/sub&gt;,e&lt;sub&gt;2&lt;/sub&gt;), where b=base, m=mantissa, e&lt;sub&gt;1&lt;/sub&gt;=minimum exponent and e&lt;sub&gt;2&lt;/sub&gt;=maximum exponent.</traducao>
  </sentenca>
  <sentenca xml:id="XML_EXIBE_PTOFLU_MSG07">
    <traducao xml:lang="pt-br">Dados para somar dois números em ponto flutuante, a partir de um dado sistema de ponto flutuante
        F(b,m,e&lt;sub&gt;inf&lt;/sub&gt;,e&lt;sub&gt;sup&lt;/sub&gt;), onde b=base, m=mantissa, e&lt;sub&gt;inf&lt;/sub&gt;=expoente inferior e e&lt;sub&gt;sup&lt;/sub&gt;=expoente superior.</traducao>
    <traducao xml:lang="en-us">Data to add two numbers in floating point, from a given floating point system
        F(b,m,e&lt;sub&gt;1&lt;/sub&gt;,e&lt;sub&gt;2&lt;/sub&gt;), where b=base, m=mantissa, e&lt;sub&gt;1&lt;/sub&gt;=minimum exponent and e&lt;sub&gt;2&lt;/sub&gt;=maximum exponent.</traducao>
  </sentenca>
  <sentenca xml:id="XML_EXIBE_PTOFLU_MSG08">
    <traducao xml:lang="pt-br">Dados para subtrair dois números em ponto flutuante, a partir de um dado sistema de ponto flutuante
        F(b,m,e&lt;sub&gt;inf&lt;/sub&gt;,e&lt;sub&gt;sup&lt;/sub&gt;), onde b=base, m=mantissa, e&lt;sub&gt;inf&lt;/sub&gt;=expoente inferior e e&lt;sub&gt;sup&lt;/sub&gt;=expoente superior.</traducao>
    <traducao xml:lang="en-us">Data to subtract two numbers in floating point, from a given floating point system
        F(b,m,e&lt;sub&gt;1&lt;/sub&gt;,e&lt;sub&gt;2&lt;/sub&gt;), where b=base, m=mantissa, e&lt;sub&gt;1&lt;/sub&gt;=minimum exponent and e&lt;sub&gt;2&lt;/sub&gt;=maximum exponent.</traducao>
  </sentenca>
  <sentenca xml:id="XML_TITLE_INTERPOLACAO">
    <traducao xml:lang="pt-br">Interpolação Polinomial</traducao>
    <traducao xml:lang="en-us">Polinomial Interpolation</traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_INTERPOLACAO_SUBTITLE_1">
    <traducao xml:lang="pt-br">Método de Newton</traducao>
    <traducao xml:lang="en-us">Newton Method - Divided Differences</traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_INTERPOLACAO_SUBTITLE_2">
    <traducao xml:lang="pt-br">Método de Lagrange</traducao>
    <traducao xml:lang="en-us">Lagrange Method</traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_INTERPOLACAO_SUBTITLE_3">
    <traducao xml:lang="pt-br">Método Splines Cúbicos</traducao>
    <traducao xml:lang="en-us">Cubic Splines Method</traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_INTERPOLACAO_MSG01">
    <traducao xml:lang="pt-br">Selecione uma opção para entrada de dados:</traducao>
    <traducao xml:lang="en-us">Select an option to input data:</traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_INTERPOLACAO_MSG02">
    <traducao xml:lang="pt-br">Caso discreto (através de um conjunto de pontos)</traducao>
    <traducao xml:lang="en-us">Discrete case (through a set of points)</traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_INTERPOLACAO_MSG03">
    <traducao xml:lang="pt-br">Caso contínuo (através de uma função e um intervalo)</traducao>
    <traducao xml:lang="en-us">Continuous case (through a function and an interval)</traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_INTERPOLACAO_MSG04">
    <traducao xml:lang="pt-br">Número de pontos:</traducao>
    <traducao xml:lang="en-us">Number of pointS:</traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_INTERPOLACAO_MSG05">
    <traducao xml:lang="pt-br">Função de entrada:</traducao>
    <traducao xml:lang="en-us">Input function:</traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_INTERPOLACAO_MSG06">
    <traducao xml:lang="pt-br">&gt;&gt;Funções Reconhecidas&lt;&lt;</traducao>
    <traducao xml:lang="en-us">&gt;&gt;Recognized Functions&lt;&lt;</traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_INTERPOLACAO_MSG07">
    <traducao xml:lang="pt-br">Intervalo de Aproximação:</traducao>
    <traducao xml:lang="en-us">Approximation Interval:</traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_INTERPOLACAO_MSG08">
    <traducao xml:lang="pt-br">Função de entrada:</traducao>
    <traducao xml:lang="en-us">Input Function:</traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_INTERPOLACAO_MSG09">
    <traducao xml:lang="pt-br">Número de pontos:</traducao>
    <traducao xml:lang="en-us">Number of points:</traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_INTERPOLACAO_MSG010">
    <traducao xml:lang="pt-br">Tipo de Distribuição do(s) </traducao>
    <traducao xml:lang="en-us">Type of distribution of</traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_INTERPOLACAO_MSG011">
    <traducao xml:lang="pt-br"> ponto(s) no intervalo: </traducao>
    <traducao xml:lang="en-us"> point(s) in interval: </traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_INTERPOLACAO_MSG012">
    <traducao xml:lang="pt-br">Distribuição uniforme</traducao>
    <traducao xml:lang="en-us">Uniform Distribution</traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_INTERPOLACAO_MSG013">
    <traducao xml:lang="pt-br">Distribuição de Chebyshev</traducao>
    <traducao xml:lang="en-us">Chebyshev Distribution</traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_INTERPOLACAO_MSG015">
    <traducao xml:lang="pt-br">Descrição dos Dados:</traducao>
    <traducao xml:lang="en-us">Data description:</traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_INTERPOLACAO_MSG016">
    <traducao xml:lang="pt-br">Número de pontos:</traducao>
    <traducao xml:lang="en-us">Number of points:</traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_INTERPOLACAO_MSG017">
    <traducao xml:lang="pt-br">Coordenadas (x,y) de cada ponto:</traducao>
    <traducao xml:lang="en-us">Coordinates (x,y) of each point:</traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_INTERPOLACAO_MSG018">
    <traducao xml:lang="pt-br">Valor a ser interpolado =</traducao>
    <traducao xml:lang="en-us">Value to be Interpolated =</traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_INTERPOLACAO_MSG019">
    <traducao xml:lang="pt-br">Descrição dos Dados:</traducao>
    <traducao xml:lang="en-us">Data description:</traducao>
  </sentenca>
  <sentenca xml:id="XML_EXIBE_INTERPOLACAO_SUBTITLE_1">
    <traducao xml:lang="pt-br">Método de Newton - Diferenças Divididas</traducao>
    <traducao xml:lang="en-us">Newton Method - Divided Differences</traducao>
  </sentenca>
  <sentenca xml:id="XML_EXIBE_INTERPOLACAO_SUBTITLE_2">
    <traducao xml:lang="pt-br">Método de Lagrange</traducao>
    <traducao xml:lang="en-us">Lagrange Method</traducao>
  </sentenca>
  <sentenca xml:id="XML_EXIBE_INTERPOLACAO_SUBTITLE_3">
    <traducao xml:lang="pt-br">Método Splines Cúbicos</traducao>
    <traducao xml:lang="en-us">Cubic Splines Method</traducao>
  </sentenca>
  <sentenca xml:id="XML_EXIBE_INTERPOLACAO_MSG01">
    <traducao xml:lang="pt-br">Exemplo </traducao>
    <traducao xml:lang="en-us">Example </traducao>
  </sentenca>
  <sentenca xml:id="XML_EXIBE_INTERPOLACAO_MSG02">
    <traducao xml:lang="pt-br"> - Caso </traducao>
    <traducao xml:lang="en-us"> - Case</traducao>
  </sentenca>
  <sentenca xml:id="XML_EXIBE_INTERPOLACAO_MSG03">
    <traducao xml:lang="pt-br">Discreto</traducao>
    <traducao xml:lang="en-us">Discrete</traducao>
  </sentenca>
  <sentenca xml:id="XML_EXIBE_INTERPOLACAO_MSG04">
    <traducao xml:lang="pt-br">Contínuo</traducao>
    <traducao xml:lang="en-us">Continuous</traducao>
  </sentenca>
  <sentenca xml:id="XML_EXIBE_INTERPOLACAO_MSG05">
    <traducao xml:lang="pt-br">Descrição:</traducao>
    <traducao xml:lang="en-us">Description:</traducao>
  </sentenca>
  <sentenca xml:id="XML_EXIBE_INTERPOLACAO_MSG06">
    <traducao xml:lang="pt-br">Função de entrada:</traducao>
    <traducao xml:lang="en-us">Input function:</traducao>
  </sentenca>
  <sentenca xml:id="XML_EXIBE_INTERPOLACAO_MSG07">
    <traducao xml:lang="pt-br">Número de pontos:</traducao>
    <traducao xml:lang="en-us">Number of points:</traducao>
  </sentenca>
  <sentenca xml:id="XML_EXIBE_INTERPOLACAO_MSG08">
    <traducao xml:lang="pt-br">Tipo de Distribuição do(s) </traducao>
    <traducao xml:lang="en-us">Type of distribution of </traducao>
  </sentenca>
  <sentenca xml:id="XML_EXIBE_INTERPOLACAO_MSG09">
    <traducao xml:lang="pt-br"> ponto(s) no intervalo: </traducao>
    <traducao xml:lang="en-us"> point(s) in interval: </traducao>
  </sentenca>
  <sentenca xml:id="XML_EXIBE_INTERPOLACAO_MSG010">
    <traducao xml:lang="pt-br">Distribuição uniforme</traducao>
    <traducao xml:lang="en-us">Uniform Distribution</traducao>
  </sentenca>
  <sentenca xml:id="XML_EXIBE_INTERPOLACAO_MSG011">
    <traducao xml:lang="pt-br">Distribuição de Chebyshev</traducao>
    <traducao xml:lang="en-us">Chebyshev Distribution</traducao>
  </sentenca>
  <sentenca xml:id="XML_EXIBE_INTERPOLACAO_MSG012">
    <traducao xml:lang="pt-br">Valor a ser interpolado =</traducao>
    <traducao xml:lang="en-us">Value to be Interpolated =</traducao>
  </sentenca>
  <sentenca xml:id="XML_EXIBE_INTERPOLACAO_MSG014">
    <traducao xml:lang="pt-br">Coordenadas (x,y) de cada ponto:</traducao>
    <traducao xml:lang="en-us">Coordinates (x,y) of each point:</traducao>
  </sentenca>
  <sentenca xml:id="XML_TITLE_EQNL">
    <traducao xml:lang="pt-br">Resolução de Equações Não-Lineares</traducao>
    <traducao xml:lang="en-us">Resolution of Nonlinear Equations</traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_EQNL_SUBTITLE_1">
    <traducao xml:lang="pt-br">Método da Secante</traducao>
    <traducao xml:lang="en-us">Secant Method</traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_EQNL_SUBTITLE_2">
    <traducao xml:lang="pt-br">Método da Bissecção</traducao>
    <traducao xml:lang="en-us">Bissection Method</traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_EQNL_SUBTITLE_3">
    <traducao xml:lang="pt-br">Método de Newton</traducao>
    <traducao xml:lang="en-us">Newton's Method</traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_EQNL_MSG01">
    <traducao xml:lang="pt-br">Selecione uma opção para entrada de dados:</traducao>
    <traducao xml:lang="en-us">Select an option to input data:</traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_EQNL_MSG02">
    <traducao xml:lang="pt-br">Através de um polinômio</traducao>
    <traducao xml:lang="en-us">Through a polynom</traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_EQNL_MSG03">
    <traducao xml:lang="pt-br">Através de uma função</traducao>
    <traducao xml:lang="en-us">Through a function</traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_EQNL_MSG04">
    <traducao xml:lang="pt-br">Grau do polinômio:</traducao>
    <traducao xml:lang="en-us">Polynom degree:</traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_EQNL_MSG05">
    <traducao xml:lang="pt-br">Coeficientes da equação:</traducao>
    <traducao xml:lang="en-us">Equation coefficients:</traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_EQNL_MSG06">
    <traducao xml:lang="pt-br">Função de entrada:</traducao>
    <traducao xml:lang="en-us">Input function:</traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_EQNL_MSG07">
    <traducao xml:lang="pt-br">&gt;&gt;Funções Reconhecidas&lt;&lt;</traducao>
    <traducao xml:lang="en-us">&gt;&gt;Recognized Functions&lt;&lt;</traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_EQNL_MSG08">
    <traducao xml:lang="pt-br">Erro relativo:</traducao>
    <traducao xml:lang="en-us">Relative error:</traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_EQNL_MSG09">
    <traducao xml:lang="pt-br">Número máximo de iterações:</traducao>
    <traducao xml:lang="en-us">Maximum number of iterations:</traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_EQNL_MSG010">
    <traducao xml:lang="pt-br">Estimativa inicial:</traducao>
    <traducao xml:lang="en-us">Initial estimative:</traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_EQNL_MSG011">
    <traducao xml:lang="pt-br">Descrição dos Dados:</traducao>
    <traducao xml:lang="en-us">Data description:</traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_EQNL_MSG012">
    <traducao xml:lang="pt-br">Intervalo desejado:</traducao>
    <traducao xml:lang="en-us">Desired interval:</traducao>
  </sentenca>
  <sentenca xml:id="XML_EXIBE_EQNL_SUBTITLE_1">
    <traducao xml:lang="pt-br">Método da Secante</traducao>
    <traducao xml:lang="en-us">Secant Method</traducao>
  </sentenca>
  <sentenca xml:id="XML_EXIBE_EQNL_SUBTITLE_2">
    <traducao xml:lang="pt-br">Método da Bissecção</traducao>
    <traducao xml:lang="en-us">Bissection Method</traducao>
  </sentenca>
  <sentenca xml:id="XML_EXIBE_EQNL_SUBTITLE_3">
    <traducao xml:lang="pt-br">Método de Newton</traducao>
    <traducao xml:lang="en-us">Newton Method</traducao>
  </sentenca>
  <sentenca xml:id="XML_EXIBE_EQNL_MSG01">
    <traducao xml:lang="pt-br">Exemplo</traducao>
    <traducao xml:lang="en-us">Example</traducao>
  </sentenca>
  <sentenca xml:id="XML_EXIBE_EQNL_MSG02">
    <traducao xml:lang="pt-br"> - Através de um </traducao>
    <traducao xml:lang="en-us"> - Through a </traducao>
  </sentenca>
  <sentenca xml:id="XML_EXIBE_EQNL_MSG03">
    <traducao xml:lang="pt-br"> polinômio</traducao>
    <traducao xml:lang="en-us"> polynom</traducao>
  </sentenca>
  <sentenca xml:id="XML_EXIBE_EQNL_MSG04">
    <traducao xml:lang="pt-br">a função</traducao>
    <traducao xml:lang="en-us">function</traducao>
  </sentenca>
  <sentenca xml:id="XML_EXIBE_EQNL_MSG05">
    <traducao xml:lang="pt-br">Função de entrada:</traducao>
    <traducao xml:lang="en-us">Input function:</traducao>
  </sentenca>
  <sentenca xml:id="XML_EXIBE_EQNL_MSG06">
    <traducao xml:lang="pt-br">Grau do polinômio:</traducao>
    <traducao xml:lang="en-us">Polynom degree:</traducao>
  </sentenca>
  <sentenca xml:id="XML_EXIBE_EQNL_MSG07">
    <traducao xml:lang="pt-br">Coeficientes da equação:</traducao>
    <traducao xml:lang="en-us">Equation coefficients:</traducao>
  </sentenca>
  <sentenca xml:id="XML_EXIBE_EQNL_MSG08">
    <traducao xml:lang="pt-br">Erro relativo:</traducao>
    <traducao xml:lang="en-us">Relative error:</traducao>
  </sentenca>
  <sentenca xml:id="XML_EXIBE_EQNL_MSG09">
    <traducao xml:lang="pt-br">Número máximo de iterações:</traducao>
    <traducao xml:lang="en-us">Maximum number of iterations:</traducao>
  </sentenca>
  <sentenca xml:id="XML_EXIBE_EQNL_MSG10">
    <traducao xml:lang="pt-br">Descrição: </traducao>
    <traducao xml:lang="en-us">Description:</traducao>
  </sentenca>
  <sentenca xml:id="XML_TITLE_SEQNL">
    <traducao xml:lang="pt-br">Sistemas de Equações Algébricas Não-Lineares</traducao>
    <traducao xml:lang="en-us">Systems of Nonlinear Algebraic Equations </traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_SEQNL_SUBTITLE_1">
    <traducao xml:lang="pt-br">Newton</traducao>
    <traducao xml:lang="en-us">Newton</traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_SEQNL_MSG01">
    <traducao xml:lang="pt-br">Número de variáveis:</traducao>
    <traducao xml:lang="en-us">Number of variables:</traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_SEQNL_MSG02">
    <traducao xml:lang="pt-br">Sistema:</traducao>
    <traducao xml:lang="en-us">System:</traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_SEQNL_MSG03">
    <traducao xml:lang="pt-br">Propriedades do Sistema :</traducao>
    <traducao xml:lang="en-us">System Properties:</traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_SEQNL_MSG04">
    <traducao xml:lang="pt-br">Verificar</traducao>
    <traducao xml:lang="en-us">Verify</traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_SEQNL_MSG05">
    <traducao xml:lang="pt-br">Tipo de Solução</traducao>
    <traducao xml:lang="en-us">Type of solution</traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_SEQNL_MSG06">
    <traducao xml:lang="pt-br">Compatível Determinado</traducao>
    <traducao xml:lang="en-us">Determined Compatible</traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_SEQNL_MSG07">
    <traducao xml:lang="pt-br">Compatível Indeterminado</traducao>
    <traducao xml:lang="en-us">Undetermined Compatible</traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_SEQNL_MSG08">
    <traducao xml:lang="pt-br">Incompatível</traducao>
    <traducao xml:lang="en-us">Incompatible</traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_SEQNL_MSG09">
    <traducao xml:lang="pt-br">Sim</traducao>
    <traducao xml:lang="en-us">Yes</traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_SEQNL_MSG010">
    <traducao xml:lang="pt-br">Não</traducao>
    <traducao xml:lang="en-us">No</traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_SEQNL_MSG011">
    <traducao xml:lang="pt-br">Simétrico:</traducao>
    <traducao xml:lang="en-us">Symetric</traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_SEQNL_MSG012">
    <traducao xml:lang="pt-br">Esparso:</traducao>
    <traducao xml:lang="en-us">Sparse:</traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_SEQNL_MSG013">
    <traducao xml:lang="pt-br">Definido Positivo:</traducao>
    <traducao xml:lang="en-us">Definite positive:</traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_SEQNL_MSG014">
    <traducao xml:lang="pt-br">Diagonalmente Dominante:</traducao>
    <traducao xml:lang="en-us">Diagonally Dominant:</traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_SEQNL_MSG015">
    <traducao xml:lang="pt-br">Número máximo de iterações:</traducao>
    <traducao xml:lang="en-us">Maximum number of iterations:</traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_SEQNL_MSG016">
    <traducao xml:lang="pt-br">&gt;k&lt;/sup&gt;&lt;/font&gt;&amp;nbsp):</traducao>
    <traducao xml:lang="en-us">Minimum precision required (enter the k value to 10&lt;sup&gt;-&lt;font size="2"&gt;k&lt;/sup&gt;&lt;/font&gt;&amp;nbsp):</traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_SEQNL_MSG017">
    <traducao xml:lang="pt-br">Precisão desejada:</traducao>
    <traducao xml:lang="en-us">Minimum precision required:</traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_SEQNL_MSG019">
    <traducao xml:lang="pt-br">Aproximações de X</traducao>
    <traducao xml:lang="en-us">X-Approximations</traducao>
  </sentenca>
  <sentenca xml:id="XML_EXIBE_SEQNL_SUBTITLE_1">
    <traducao xml:lang="pt-br">Newton</traducao>
    <traducao xml:lang="en-us">Newton</traducao>
  </sentenca>
  <sentenca xml:id="XML_EXIBE_SEQNL_MSG01">
    <traducao xml:lang="pt-br">Sistema de dimensão </traducao>
    <traducao xml:lang="en-us">System of dimension </traducao>
  </sentenca>
  <sentenca xml:id="XML_EXIBE_SEQNL_MSG02">
    <traducao xml:lang="pt-br">Número de variáveis:</traducao>
    <traducao xml:lang="en-us">Number of variables:</traducao>
  </sentenca>
  <sentenca xml:id="XML_EXIBE_SEQNL_MSG03">
    <traducao xml:lang="pt-br">Número máximo de iterações:</traducao>
    <traducao xml:lang="en-us">Maximum number of iterations:</traducao>
  </sentenca>
  <sentenca xml:id="XML_EXIBE_SEQNL_MSG04">
    <traducao xml:lang="pt-br">Precisão desejada:</traducao>
    <traducao xml:lang="en-us">Minimun desired precision:</traducao>
  </sentenca>
  <sentenca xml:id="XML_EXIBE_SEQNL_MSG05">
    <traducao xml:lang="pt-br">Sistema</traducao>
    <traducao xml:lang="en-us">System</traducao>
  </sentenca>
  <sentenca xml:id="XML_EXIBE_SEQNL_MSG06">
    <traducao xml:lang="pt-br">Aproximações de X</traducao>
    <traducao xml:lang="en-us">X-Approximations</traducao>
  </sentenca>
  <sentenca xml:id="XML_TITLE_AJDADOS">
    <traducao xml:lang="pt-br">Ajuste de Dados</traducao>
    <traducao xml:lang="en-us">Data Fitting</traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_AJDADOS_SUBTITLE_1">
    <traducao xml:lang="pt-br">Método dos Mínimos Quadrados</traducao>
    <traducao xml:lang="en-us">Least-Squares Method</traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_AJDADOS_MSG01">
    <traducao xml:lang="pt-br">Selecione uma opção para entrada de dados:</traducao>
    <traducao xml:lang="en-us">Select an option to input data:</traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_AJDADOS_MSG02">
    <traducao xml:lang="pt-br">Caso discreto (através de um conjunto de pontos)</traducao>
    <traducao xml:lang="en-us">Discrete case (through a set of points)</traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_AJDADOS_MSG03">
    <traducao xml:lang="pt-br">Caso contínuo (através de uma função e um intervalo)</traducao>
    <traducao xml:lang="en-us">Continuous case (through a function and an itnerval)</traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_AJDADOS_MSG04">
    <traducao xml:lang="pt-br">Número de pontos:</traducao>
    <traducao xml:lang="en-us">Number of points:</traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_AJDADOS_MSG05">
    <traducao xml:lang="pt-br">Função de entrada:</traducao>
    <traducao xml:lang="en-us">Input function:</traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_AJDADOS_MSG06">
    <traducao xml:lang="pt-br">Intervalo de Aproximação:</traducao>
    <traducao xml:lang="en-us">Approximation interval:</traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_AJDADOS_MSG07">
    <traducao xml:lang="pt-br">Número de pontos:</traducao>
    <traducao xml:lang="en-us">Number of points:</traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_AJDADOS_MSG08">
    <traducao xml:lang="pt-br">Coordenadas (x,y) de cada ponto:</traducao>
    <traducao xml:lang="en-us">Coordinates (x,y) of each point:</traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_AJDADOS_MSG09">
    <traducao xml:lang="pt-br">Grau do polinômio aproximador:</traducao>
    <traducao xml:lang="en-us">Approximator polynom degree:</traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_AJDADOS_MSG010">
    <traducao xml:lang="pt-br">Descrição dos Dados:</traducao>
    <traducao xml:lang="en-us">Data description:</traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_AJDADOS_MSG011">
    <traducao xml:lang="pt-br">&gt;&gt;Funções Reconhecidas&lt;&lt;</traducao>
    <traducao xml:lang="en-us">&gt;&gt;Recognized Functions&lt;&lt;</traducao>
  </sentenca>
  <sentenca xml:id="XML_EXIBE_AJDADOS_SUBTITLE_1">
    <traducao xml:lang="pt-br">Método dos Mínimos Quadrados</traducao>
    <traducao xml:lang="en-us">Least-Squares Method</traducao>
  </sentenca>
  <sentenca xml:id="XML_EXIBE_AJDADOS_MSG01">
    <traducao xml:lang="pt-br">Exemplo</traducao>
    <traducao xml:lang="en-us">Example</traducao>
  </sentenca>
  <sentenca xml:id="XML_EXIBE_AJDADOS_MSG02">
    <traducao xml:lang="pt-br"> - Caso </traducao>
    <traducao xml:lang="en-us"> - Case </traducao>
  </sentenca>
  <sentenca xml:id="XML_EXIBE_AJDADOS_MSG03">
    <traducao xml:lang="pt-br">Discreto</traducao>
    <traducao xml:lang="en-us">Discrete</traducao>
  </sentenca>
  <sentenca xml:id="XML_EXIBE_AJDADOS_MSG04">
    <traducao xml:lang="pt-br">Contínuo</traducao>
    <traducao xml:lang="en-us">Continuous</traducao>
  </sentenca>
  <sentenca xml:id="XML_EXIBE_AJDADOS_MSG05">
    <traducao xml:lang="pt-br">Descrição:</traducao>
    <traducao xml:lang="en-us">Description:</traducao>
  </sentenca>
  <sentenca xml:id="XML_EXIBE_AJDADOS_MSG06">
    <traducao xml:lang="pt-br">Função de entrada:</traducao>
    <traducao xml:lang="en-us">Input function:</traducao>
  </sentenca>
  <sentenca xml:id="XML_EXIBE_AJDADOS_MSG07">
    <traducao xml:lang="pt-br">Intervalo de Aproximação:</traducao>
    <traducao xml:lang="en-us">Approximation interval:</traducao>
  </sentenca>
  <sentenca xml:id="XML_EXIBE_AJDADOS_MSG08">
    <traducao xml:lang="pt-br">Número de pontos:</traducao>
    <traducao xml:lang="en-us">Number of points:</traducao>
  </sentenca>
  <sentenca xml:id="XML_EXIBE_AJDADOS_MSG09">
    <traducao xml:lang="pt-br">Coordenadas (x,y) de cada ponto:</traducao>
    <traducao xml:lang="en-us">Coordinates (x,y) of each point:</traducao>
  </sentenca>
  <sentenca xml:id="XML_EXIBE_AJDADOS_MSG010">
    <traducao xml:lang="pt-br">Grau do polinômio aproximador:</traducao>
    <traducao xml:lang="en-us">Approximator polynom degree:</traducao>
  </sentenca>
  <sentenca xml:id="XML_TITLE_DERIVADA">
    <traducao xml:lang="pt-br">Derivação Numérica</traducao>
    <traducao xml:lang="en-us">Numeric Derivative</traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_DERIVADA_SUBTITLE_1">
    <traducao xml:lang="pt-br">Método da Diferença Central</traducao>
    <traducao xml:lang="en-us">Central Difference Method</traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_DERIVADA_MSG01">
    <traducao xml:lang="pt-br">Função de entrada:</traducao>
    <traducao xml:lang="en-us">Input function:</traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_DERIVADA_MSG02">
    <traducao xml:lang="pt-br">&gt;&gt;Funções Reconhecidas&lt;&lt;</traducao>
    <traducao xml:lang="en-us">&gt;&gt;Recognized Functions&lt;&lt;</traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_DERIVADA_MSG03">
    <traducao xml:lang="pt-br">Calcular derivada da f(x) para x =</traducao>
    <traducao xml:lang="en-us">Calculate the derivate of f(x) at x=</traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_DERIVADA_MSG04">
    <traducao xml:lang="pt-br">Número máximo de iterações:</traducao>
    <traducao xml:lang="en-us">Maximum number of iterations:</traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_DERIVADA_MSG05">
    <traducao xml:lang="pt-br">Erro relativo da resposta:</traducao>
    <traducao xml:lang="en-us">Response relative error:</traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_DERIVADA_MSG06">
    <traducao xml:lang="pt-br">Descrição dos Dados:</traducao>
    <traducao xml:lang="en-us">Data Description:</traducao>
  </sentenca>
  <sentenca xml:id="XML_EXIBE_DERIVADA_SUBTITLE_1">
    <traducao xml:lang="pt-br">Método da Diferença Central</traducao>
    <traducao xml:lang="en-us">Central Difference Method</traducao>
  </sentenca>
  <sentenca xml:id="XML_EXIBE_DERIVADA_MSG01">
    <traducao xml:lang="pt-br">Exemplo</traducao>
    <traducao xml:lang="en-us">Example</traducao>
  </sentenca>
  <sentenca xml:id="XML_EXIBE_DERIVADA_MSG03">
    <traducao xml:lang="pt-br">Descrição: </traducao>
    <traducao xml:lang="en-us">Description: </traducao>
  </sentenca>
  <sentenca xml:id="XML_EXIBE_DERIVADA_MSG04">
    <traducao xml:lang="pt-br">Função de entrada:</traducao>
    <traducao xml:lang="en-us">Input function:</traducao>
  </sentenca>
  <sentenca xml:id="XML_EXIBE_DERIVADA_MSG05">
    <traducao xml:lang="pt-br">Funções Reconhecidas</traducao>
    <traducao xml:lang="en-us">Recognized Functions</traducao>
  </sentenca>
  <sentenca xml:id="XML_EXIBE_DERIVADA_MSG06">
    <traducao xml:lang="pt-br">Calcular derivada da f(x) para x = </traducao>
    <traducao xml:lang="en-us">Calculate the derivate of f(x) at x=</traducao>
  </sentenca>
  <sentenca xml:id="XML_EXIBE_DERIVADA_MSG07">
    <traducao xml:lang="pt-br">Número máximo de iterações: </traducao>
    <traducao xml:lang="en-us">Maximum number of iterations: </traducao>
  </sentenca>
  <sentenca xml:id="XML_EXIBE_DERIVADA_MSG08">
    <traducao xml:lang="pt-br">Erro relativo da resposta: </traducao>
    <traducao xml:lang="en-us">Responsed relative error: </traducao>
  </sentenca>
  <sentenca xml:id="XML_TITLE_INTNUM">
    <traducao xml:lang="pt-br">Integração Numérica</traducao>
    <traducao xml:lang="en-us">Numerical Integration</traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_INTNUM_SUBTITLE_1">
    <traducao xml:lang="pt-br">Método de Richardson</traducao>
    <traducao xml:lang="en-us">Richardson's Method</traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_INTNUM_SUBTITLE_2">
    <traducao xml:lang="pt-br">Método de Romberg</traducao>
    <traducao xml:lang="en-us">Romberg's Method</traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_INTNUM_SUBTITLE_3">
    <traducao xml:lang="pt-br">Método de Simpson</traducao>
    <traducao xml:lang="en-us">Simpson's Method</traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_INTNUM_SUBTITLE_4">
    <traducao xml:lang="pt-br">Método do Trapézio</traducao>
    <traducao xml:lang="en-us">Trapezoidal Method</traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_INTNUM_MSG01">
    <traducao xml:lang="pt-br">Função de entrada:</traducao>
    <traducao xml:lang="en-us">Input function:</traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_INTNUM_MSG02">
    <traducao xml:lang="pt-br">&gt;&gt;Funções Reconhecidas&lt;&lt;</traducao>
    <traducao xml:lang="en-us">&gt;&gt;Recognized Functions&lt;&lt;</traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_INTNUM_MSG03">
    <traducao xml:lang="pt-br">Limite inferior (a):</traducao>
    <traducao xml:lang="en-us">Inferior limit (a):</traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_INTNUM_MSG04">
    <traducao xml:lang="pt-br">Limite superior (b):</traducao>
    <traducao xml:lang="en-us">Upper limit (b):</traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_INTNUM_MSG05">
    <traducao xml:lang="pt-br">Número par (n) de partições do intervalo:</traducao>
    <traducao xml:lang="en-us">Even number (n) of partitions of interval:</traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_INTNUM_MSG06">
    <traducao xml:lang="pt-br">Número par (m | m &gt; n) de partições do intervalo :</traducao>
    <traducao xml:lang="en-us">Even number (m | m &gt; n) of partitions of interval:</traducao>
  </sentenca>
  <sentenca xml:id="XML_GERA_INTNUM_MSG07">
    <traducao xml:lang="pt-br">Descrição dos Dados:</traducao>
    <traducao xml:lang="en-us">Data Description:</traducao>
  </sentenca>
  <sentenca xml:id="XML_EXIBE_INTNUM_SUBTITLE_1">
    <traducao xml:lang="pt-br">Método de Richardson</traducao>
    <traducao xml:lang="en-us">Richardson's Method</traducao>
  </sentenca>
  <sentenca xml:id="XML_EXIBE_INTNUM_SUBTITLE_2">
    <traducao xml:lang="pt-br">Método de Romberg</traducao>
    <traducao xml:lang="en-us">Romberg's Method</traducao>
  </sentenca>
  <sentenca xml:id="XML_EXIBE_INTNUM_SUBTITLE_3">
    <traducao xml:lang="pt-br">Método de Simpson</traducao>
    <traducao xml:lang="en-us">Simpson's Method"</traducao>
  </sentenca>
  <sentenca xml:id="XML_EXIBE_INTNUM_SUBTITLE_4">
    <traducao xml:lang="pt-br">Método do Trapézio</traducao>
    <traducao xml:lang="en-us">Trapezoidal Method</traducao>
  </sentenca>
  <sentenca xml:id="XML_EXIBE_INTNUM_MSG01">
    <traducao xml:lang="pt-br">Exemplo</traducao>
    <traducao xml:lang="en-us">Example</traducao>
  </sentenca>
  <sentenca xml:id="XML_EXIBE_INTNUM_MSG02">
    <traducao xml:lang="pt-br">Descrição:</traducao>
    <traducao xml:lang="en-us">Description:</traducao>
  </sentenca>
  <sentenca xml:id="XML_EXIBE_INTNUM_MSG03">
    <traducao xml:lang="pt-br">Função de entrada:</traducao>
    <traducao xml:lang="en-us">Input function:</traducao>
  </sentenca>
  <sentenca xml:id="XML_EXIBE_INTNUM_MSG04">
    <traducao xml:lang="pt-br">Limite inferior (a):</traducao>
    <traducao xml:lang="en-us">Lower limit (a):</traducao>
  </sentenca>
  <sentenca xml:id="XML_EXIBE_INTNUM_MSG05">
    <traducao xml:lang="pt-br">Limite superior (b):</traducao>
    <traducao xml:lang="en-us">Upper limit (b):</traducao>
  </sentenca>
  <sentenca xml:id="XML_EXIBE_INTNUM_MSG06">
    <traducao xml:lang="pt-br">Número par (n) de partições do intervalo :</traducao>
    <traducao xml:lang="en-us">Even number (n) of partitions of interval:</traducao>
  </sentenca>
  <sentenca xml:id="XML_EXIBE_INTNUM_MSG07">
    <traducao xml:lang="pt-br">Número par (m | m &gt; n) de partições do intervalo :</traducao>
    <traducao xml:lang="en-us">Even number (m | m > n) of partitions of interval</traducao>
  </sentenca>
  <sentenca xml:id="XML_EXIBE_INTNUM_MSG08">
    <traducao xml:lang="pt-br">&gt;&gt;Funções Reconhecidas&lt;&lt;</traducao>
    <traducao xml:lang="en-us">&gt;&gt;Recognized Functions&lt;&lt;</traducao>
  </sentenca>
</strings>
